Table of Contents

  • 0  Package Install
  • 1  Dataset: Iris (붓꽃 자료)
    • 1.1  Dataset with graphs
    • 1.2  Descriptive statistics of the datasetm
    • 1.3  Euclidean Distance of the dataset
  • 2  Weighted Maxcut
    • 2.1  Example: Fully Connected Graph with Randomized weight
    • 2.2  Brute Force Algorithms to Calculate Optimal Solution
  • 3  QAOA solving Weighted Maxcut
  • 4  Simulating with Different P-Values
  • 5  Clustering using QAOA-Weighted Maxcut with Iris Data
    • 5.1  Method 1: Brute Force Algorithms to Calculate Optimal Solution
    • 5.2  Method 2: QAOA
    • 5.3  Comparison with K-means Clustering
    • 5.4  Silhoutte Score
      • 5.4.1  Code with example
      • 5.4.2  Brute Force - Silhoutte Score
      • 5.4.3  QAOA - Silhoutte Score
      • 5.4.4  K-Means - Silhoutte Score
      • 5.4.5  True Label- Silhoutte Score
    • 5.5  Dunn Index
      • 5.5.1  Code with example
        • 5.5.1.1  클러스터 내 거리 측도 Intra-Cluster distance measure
        • 5.5.1.2  클러스터 간 거리 측도 Inter-Cluster distance measure
      • 5.5.2  Dunn Index 파이썬 구현
    • 5.6  Brute Force - Dunn Index
    • 5.7  QAOA - Dunn Index
    • 5.8  K-Means - Dunn Index
    • 5.9  True Label - Dunn Index

Package Install¶

In [1]:
# !pip install numpy
# !pip install pandas
# !pip install sklearn

# !pip install qiskit

Dataset: Iris (붓꽃 자료)¶

  • We then load the Iris data set. There is a bit of preprocessing to do in order to encode the inputs into the amplitudes of a quantum state. In the last preprocessing step, we translate the inputs x to rotation angles using the get_angles function we defined above.

Iris-Dataset-Classification.png

  • image source: https://www.embedded-robotics.com/iris-dataset-classification/

  • X variables: [Sepal length, Sepal width, Petal length, Petal width], (각 Sepal: 꽃받침, Petal: 꽃잎 의 가로, 세로 길이)

  • Y variable: Species of iris flowers (0:"setosa", 1:"versicolor", 2:"virginica")
  • We are trying to classify iris flowers to correct type of iris flowers using the lengths of various parts of the flower.
In [2]:
from sklearn.datasets import load_iris
import pandas as pd
import numpy as np

# visualization package
import matplotlib.pyplot as plt
import seaborn as sns

# sample data load
iris = load_iris()

# pring out data with variable types and its description
# print(iris)
In [3]:
# Description of the dataset
print(iris.DESCR)

.. _iris_dataset:

Iris plants dataset
--------------------

**Data Set Characteristics:**

    :Number of Instances: 150 (50 in each of three classes)
    :Number of Attributes: 4 numeric, predictive attributes and the class
    :Attribute Information:
        - sepal length in cm
        - sepal width in cm
        - petal length in cm
        - petal width in cm
        - class:
                - Iris-Setosa
                - Iris-Versicolour
                - Iris-Virginica
                
    :Summary Statistics:

    ============== ==== ==== ======= ===== ====================
                    Min  Max   Mean    SD   Class Correlation
    ============== ==== ==== ======= ===== ====================
    sepal length:   4.3  7.9   5.84   0.83    0.7826
    sepal width:    2.0  4.4   3.05   0.43   -0.4194
    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)
    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)
    ============== ==== ==== ======= ===== ====================

    :Missing Attribute Values: None
    :Class Distribution: 33.3% for each of 3 classes.
    :Creator: R.A. Fisher
    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)
    :Date: July, 1988

The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken
from Fisher's paper. Note that it's the same as in R, but not as in the UCI
Machine Learning Repository, which has two wrong data points.

This is perhaps the best known database to be found in the
pattern recognition literature.  Fisher's paper is a classic in the field and
is referenced frequently to this day.  (See Duda & Hart, for example.)  The
data set contains 3 classes of 50 instances each, where each class refers to a
type of iris plant.  One class is linearly separable from the other 2; the
latter are NOT linearly separable from each other.

.. topic:: References

   - Fisher, R.A. "The use of multiple measurements in taxonomic problems"
     Annual Eugenics, 7, Part II, 179-188 (1936); also in "Contributions to
     Mathematical Statistics" (John Wiley, NY, 1950).
   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.
     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.
   - Dasarathy, B.V. (1980) "Nosing Around the Neighborhood: A New System
     Structure and Classification Rule for Recognition in Partially Exposed
     Environments".  IEEE Transactions on Pattern Analysis and Machine
     Intelligence, Vol. PAMI-2, No. 1, 67-71.
   - Gates, G.W. (1972) "The Reduced Nearest Neighbor Rule".  IEEE Transactions
     on Information Theory, May 1972, 431-433.
   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al"s AUTOCLASS II
     conceptual clustering system finds 3 classes in the data.
   - Many, many more ...

Dataset with graphs¶

In [4]:
# feature_names(x variables) 와 target(y variable)을 잘 나타내도록 data frame 생성
data_iris = pd.DataFrame(data=iris.data, columns=iris.feature_names)
data_iris['species'] = iris.target

# Mapping the labels-'species' with numbers
data_iris['species'] = data_iris['species'].map(
    {0: "setosa", 1: "versicolor", 2: "virginica"})
print(data_iris)

# Plot scatter plots and density distribution plots feature-wise WITH labels
sns.set(font_scale=1.5)
sns.pairplot(data_iris, hue="species", height=3)
plt.show()

     sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)  \
0                  5.1               3.5                1.4               0.2   
1                  4.9               3.0                1.4               0.2   
2                  4.7               3.2                1.3               0.2   
3                  4.6               3.1                1.5               0.2   
4                  5.0               3.6                1.4               0.2   
..                 ...               ...                ...               ...   
145                6.7               3.0                5.2               2.3   
146                6.3               2.5                5.0               1.9   
147                6.5               3.0                5.2               2.0   
148                6.2               3.4                5.4               2.3   
149                5.9               3.0                5.1               1.8   

       species  
0       setosa  
1       setosa  
2       setosa  
3       setosa  
4       setosa  
..         ...  
145  virginica  
146  virginica  
147  virginica  
148  virginica  
149  virginica  

[150 rows x 5 columns]
In [5]:
# Plot scatter plots and density distribution plots feature-wise WITHOUT any labels
sns.set(font_scale=1.5)
sns.pairplot(data_iris, height=3)
plt.show()

Descriptive statistics of the datasetm¶

In [6]:
# Descriptive statistics of the dataset
data_iris.describe()
Out[6]:
sepal length (cm) sepal width (cm) petal length (cm) petal width (cm)
count 150.000000 150.000000 150.000000 150.000000
mean 5.843333 3.057333 3.758000 1.199333
std 0.828066 0.435866 1.765298 0.762238
min 4.300000 2.000000 1.000000 0.100000
25% 5.100000 2.800000 1.600000 0.300000
50% 5.800000 3.000000 4.350000 1.300000
75% 6.400000 3.300000 5.100000 1.800000
max 7.900000 4.400000 6.900000 2.500000
In [7]:
data_iris['species'].value_counts()

# pd.crosstab(index=data_iris['species'], columns="count")
Out[7]:
setosa        50
versicolor    50
virginica     50
Name: species, dtype: int64

Euclidean Distance of the dataset¶

In [8]:
# Calculate the Euclidean distance of the data
iris_euclidean_dist = np.linalg.norm(data_iris.iloc[:, 0:4].values, axis=1)
iris_euclidean_dist
Out[8]:
array([ 6.34507683,  5.91692488,  5.83609458,  5.7497826 ,  6.32139225,
        6.88621812,  5.8966092 ,  6.23297682,  5.45618915,  5.98999165,
        6.71863081,  6.09918027,  5.83180932,  5.35817133,  7.14982517,
        7.36613874,  6.79852925,  6.34901567,  7.06470098,  6.54140658,
        6.60681466,  6.48922183,  5.92958683,  6.32771681,  6.18465844,
        6.04979338,  6.26737585,  6.44825558,  6.37181293,  5.91016074,
        5.93717104,  6.56734345,  6.79043445,  7.06328535,  5.99249531,
        6.05970296,  6.65056389,  6.2401923 ,  5.48543526,  6.31347765,
        6.24739946,  5.22685374,  5.59732079,  6.33798075,  6.64981203,
        5.83866423,  6.56124988,  5.77927331,  6.63852393,  6.15548536,
        9.12633552,  8.58487041,  9.13673902,  7.29588925,  8.5732141 ,
        7.89113427,  8.67352293,  6.45445583,  8.64985549,  7.17635005,
        6.5       ,  7.98122798,  7.60526134,  8.3468557 ,  7.37699126,
        8.70746806,  7.92842986,  7.6642025 ,  8.11048704,  7.35051019,
        8.44570897,  7.92085854,  8.49705831,  8.28130425,  8.33966426,
        8.59534758,  8.89269363,  9.04322951,  8.1798533 ,  7.24568837,
        7.18748913,  7.12039325,  7.58814865,  8.47702778,  7.78845299,
        8.38868285,  8.87918915,  8.12588457,  7.67202711,  7.36138574,
        7.60328876,  8.32646384,  7.60526134,  6.49461315,  7.61445993,
        7.78267306,  7.76079893,  8.18718511,  6.5169011 ,  7.67007171,
        9.63483264,  8.39940474,  9.93126377,  9.09395404,  9.47259204,
       10.71120908,  7.30753036, 10.22888068,  9.38189746, 10.40480658,
        9.08295106,  8.94147639,  9.48156105,  8.23043134,  8.55862138,
        9.19673855,  9.20543318, 11.11125555, 10.90642013,  8.2516665 ,
        9.77905926,  8.19817053, 10.77125805,  8.61568337,  9.62704524,
       10.06578363,  8.51821578,  8.57088093,  9.19619487,  9.85088828,
       10.16956243, 11.03675677,  9.21954446,  8.70574523,  8.79147314,
       10.52568288,  9.4005319 ,  9.16842407,  8.44274837,  9.52837867,
        9.57183368,  9.40850679,  8.39940474,  9.8275124 ,  9.72213968,
        9.28547252,  8.63423419,  9.07138358,  9.18966811,  8.54751426])
In [9]:
# Create new column of Euclidean distance
data_iris['Euclid_dist'] = iris_euclidean_dist
data_iris['Euclid_dist_sq'] = iris_euclidean_dist**2
In [10]:
# # Function that calculates Mahalanobis distance
# def mahalanobis(x=None, data=None, cov=None):
#     x_mu = x - x.mean()
#     if not cov:
#         cov = np.cov(data.values.T)
#     inv_covmat = np.linalg.inv(cov)
#     left = np.dot(x_mu, inv_covmat)
#     mahal = np.dot(left, x_mu.T)
#     return mahal.diagonal()
In [11]:
# # Calculate the Mahalanobis distance of the data
# Mahal_dist = mahalanobis(x=data_iris.iloc[:,range(4)], data=data_iris.iloc[:,range(4)])
# Mahal_dist
In [12]:
# # Create new column of Mahalanobis distance
# data_iris['Mahal_dist'] = Mahal_dist
# data_iris['Mahal_dist_sq'] = Mahal_dist**2
In [13]:
data_iris[['species', 'Euclid_dist', 'Euclid_dist_sq']]
# data_iris[['species', 'Euclid_dist','Euclid_dist_sq','Mahal_dist', 'Mahal_dist_sq']]
Out[13]:
species Euclid_dist Euclid_dist_sq
0 setosa 6.345077 40.26
1 setosa 5.916925 35.01
2 setosa 5.836095 34.06
3 setosa 5.749783 33.06
4 setosa 6.321392 39.96
... ... ... ...
145 virginica 9.285473 86.22
146 virginica 8.634234 74.55
147 virginica 9.071384 82.29
148 virginica 9.189668 84.45
149 virginica 8.547514 73.06

150 rows × 3 columns

In [14]:
# Plot scatter plots and density distribution plots feature-wise WITH labels
sns.set(font_scale=1.5)
sns.pairplot(data_iris, hue="species", height=3)
plt.show()
In [15]:
# Plot scatter plots and density distribution plots feature-wise WITHOUT any labels
sns.set(font_scale=1.5)
sns.pairplot(data_iris, height=3)
plt.show()
In [16]:
sns.pairplot(data_iris[['species', 'Euclid_dist',
             'Euclid_dist_sq']], hue="species", height=3)
# sns.pairplot(data_iris[['species', 'Euclid_dist', 'Euclid_dist_sq', 'Mahal_dist','Mahal_dist_sq']], hue="species", height=3)
Out[16]:
<seaborn.axisgrid.PairGrid at 0x17a5691d490>
In [17]:
sns.pairplot(data_iris[['species', 'Euclid_dist', 'Euclid_dist_sq']], height=3)
# sns.pairplot(data_iris[['species', 'Euclid_dist', 'Euclid_dist_sq', 'Mahal_dist','Mahal_dist_sq']], height=3)
Out[17]:
<seaborn.axisgrid.PairGrid at 0x17a579a0700>
In [ ]:

Weighted Maxcut¶

Example: Fully Connected Graph with Randomized weight¶

In [18]:
import networkx as nx
import numpy as np
import matplotlib.pyplot as plt


def draw_graph(G, col, pos):
    plt.figure(figsize=(12, 8))
    default_axes = plt.axes(frameon=True)
    nx.draw_networkx(G, node_color=col, node_size=600,
                     alpha=0.8, ax=default_axes, pos=pos, font_size=16)
    edge_labels = nx.get_edge_attributes(G, 'weight')
    nx.draw_networkx_edge_labels(
        G, pos=pos, edge_labels=edge_labels, font_size=16)


n = 6  # number of nodes in graph

np.random.seed(150)
edge_weights = np.random.randint(1, 5, size=(n, n))
edge_weights = edge_weights * edge_weights.T / 2

G = nx.Graph()
G.add_nodes_from(np.arange(0, n, 1))
for i in range(n):
    for j in range(n):
        if i > j:
            G.add_edge(i, j, weight=edge_weights[i, j])

colors = ['g' for node in G.nodes()]
pos = nx.spring_layout(G)
In [19]:
# graph G: nodes
G.nodes
Out[19]:
NodeView((0, 1, 2, 3, 4, 5))
In [20]:
# graph G: edges
G.edges
Out[20]:
EdgeView([(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 5)])
In [21]:
# graph G: edges with weights
G.edges.data()
Out[21]:
EdgeDataView([(0, 1, {'weight': 1.5}), (0, 2, {'weight': 6.0}), (0, 3, {'weight': 1.0}), (0, 4, {'weight': 0.5}), (0, 5, {'weight': 3.0}), (1, 2, {'weight': 6.0}), (1, 3, {'weight': 3.0}), (1, 4, {'weight': 2.0}), (1, 5, {'weight': 2.0}), (2, 3, {'weight': 0.5}), (2, 4, {'weight': 4.0}), (2, 5, {'weight': 4.0}), (3, 4, {'weight': 2.0}), (3, 5, {'weight': 4.0}), (4, 5, {'weight': 6.0})])
In [22]:
# Plot of the give graph G
draw_graph(G, colors, pos)
In [23]:
# Adjacency matrix of weighted graph
w = np.zeros([n, n])
for i in range(n):
    for j in range(n):
        temp = G.get_edge_data(i, j, default=0)
        if temp != 0:
            w[i, j] = temp['weight']

w
Out[23]:
array([[0. , 1.5, 6. , 1. , 0.5, 3. ],
       [1.5, 0. , 6. , 3. , 2. , 2. ],
       [6. , 6. , 0. , 0.5, 4. , 4. ],
       [1. , 3. , 0.5, 0. , 2. , 4. ],
       [0.5, 2. , 4. , 2. , 0. , 6. ],
       [3. , 2. , 4. , 4. , 6. , 0. ]])

Brute Force Algorithms to Calculate Optimal Solution¶

In [24]:
best_cost_brute = 0
for b in range(2**n):
    x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]
    cost = 0
    for i in range(n):
        for j in range(n):
            cost = cost + w[i, j] * x[i] * (1-x[j])
    if best_cost_brute < cost:
        best_cost_brute = cost
        xbest_brute = x
    print('case =', '%-20s' % str(x), ' cost =', '%-6s' %
          str(cost), ' try =', str(b+1))

colors_brute = ['g' if xbest_brute[i] == 0 else 'c' for i in range(n)]
print('\nBest case(solution) =', '%-20s' %
      str(xbest_brute), ' cost =', '%-6s' % str(best_cost_brute))

case = [0, 0, 0, 0, 0, 0]    cost = 0.0     try = 1
case = [1, 0, 0, 0, 0, 0]    cost = 12.0    try = 2
case = [0, 1, 0, 0, 0, 0]    cost = 14.5    try = 3
case = [1, 1, 0, 0, 0, 0]    cost = 23.5    try = 4
case = [0, 0, 1, 0, 0, 0]    cost = 20.5    try = 5
case = [1, 0, 1, 0, 0, 0]    cost = 20.5    try = 6
case = [0, 1, 1, 0, 0, 0]    cost = 23.0    try = 7
case = [1, 1, 1, 0, 0, 0]    cost = 20.0    try = 8
case = [0, 0, 0, 1, 0, 0]    cost = 10.5    try = 9
case = [1, 0, 0, 1, 0, 0]    cost = 20.5    try = 10
case = [0, 1, 0, 1, 0, 0]    cost = 19.0    try = 11
case = [1, 1, 0, 1, 0, 0]    cost = 26.0    try = 12
case = [0, 0, 1, 1, 0, 0]    cost = 30.0    try = 13
case = [1, 0, 1, 1, 0, 0]    cost = 28.0    try = 14
case = [0, 1, 1, 1, 0, 0]    cost = 26.5    try = 15
case = [1, 1, 1, 1, 0, 0]    cost = 21.5    try = 16
case = [0, 0, 0, 0, 1, 0]    cost = 14.5    try = 17
case = [1, 0, 0, 0, 1, 0]    cost = 25.5    try = 18
case = [0, 1, 0, 0, 1, 0]    cost = 25.0    try = 19
case = [1, 1, 0, 0, 1, 0]    cost = 33.0    try = 20
case = [0, 0, 1, 0, 1, 0]    cost = 27.0    try = 21
case = [1, 0, 1, 0, 1, 0]    cost = 26.0    try = 22
case = [0, 1, 1, 0, 1, 0]    cost = 25.5    try = 23
case = [1, 1, 1, 0, 1, 0]    cost = 21.5    try = 24
case = [0, 0, 0, 1, 1, 0]    cost = 21.0    try = 25
case = [1, 0, 0, 1, 1, 0]    cost = 30.0    try = 26
case = [0, 1, 0, 1, 1, 0]    cost = 25.5    try = 27
case = [1, 1, 0, 1, 1, 0]    cost = 31.5    try = 28
case = [0, 0, 1, 1, 1, 0]    cost = 32.5    try = 29
case = [1, 0, 1, 1, 1, 0]    cost = 29.5    try = 30
case = [0, 1, 1, 1, 1, 0]    cost = 25.0    try = 31
case = [1, 1, 1, 1, 1, 0]    cost = 19.0    try = 32
case = [0, 0, 0, 0, 0, 1]    cost = 19.0    try = 33
case = [1, 0, 0, 0, 0, 1]    cost = 25.0    try = 34
case = [0, 1, 0, 0, 0, 1]    cost = 29.5    try = 35
case = [1, 1, 0, 0, 0, 1]    cost = 32.5    try = 36
case = [0, 0, 1, 0, 0, 1]    cost = 31.5    try = 37
case = [1, 0, 1, 0, 0, 1]    cost = 25.5    try = 38
case = [0, 1, 1, 0, 0, 1]    cost = 30.0    try = 39
case = [1, 1, 1, 0, 0, 1]    cost = 21.0    try = 40
case = [0, 0, 0, 1, 0, 1]    cost = 21.5    try = 41
case = [1, 0, 0, 1, 0, 1]    cost = 25.5    try = 42
case = [0, 1, 0, 1, 0, 1]    cost = 26.0    try = 43
case = [1, 1, 0, 1, 0, 1]    cost = 27.0    try = 44
case = [0, 0, 1, 1, 0, 1]    cost = 33.0    try = 45
case = [1, 0, 1, 1, 0, 1]    cost = 25.0    try = 46
case = [0, 1, 1, 1, 0, 1]    cost = 25.5    try = 47
case = [1, 1, 1, 1, 0, 1]    cost = 14.5    try = 48
case = [0, 0, 0, 0, 1, 1]    cost = 21.5    try = 49
case = [1, 0, 0, 0, 1, 1]    cost = 26.5    try = 50
case = [0, 1, 0, 0, 1, 1]    cost = 28.0    try = 51
case = [1, 1, 0, 0, 1, 1]    cost = 30.0    try = 52
case = [0, 0, 1, 0, 1, 1]    cost = 26.0    try = 53
case = [1, 0, 1, 0, 1, 1]    cost = 19.0    try = 54
case = [0, 1, 1, 0, 1, 1]    cost = 20.5    try = 55
case = [1, 1, 1, 0, 1, 1]    cost = 10.5    try = 56
case = [0, 0, 0, 1, 1, 1]    cost = 20.0    try = 57
case = [1, 0, 0, 1, 1, 1]    cost = 23.0    try = 58
case = [0, 1, 0, 1, 1, 1]    cost = 20.5    try = 59
case = [1, 1, 0, 1, 1, 1]    cost = 20.5    try = 60
case = [0, 0, 1, 1, 1, 1]    cost = 23.5    try = 61
case = [1, 0, 1, 1, 1, 1]    cost = 14.5    try = 62
case = [0, 1, 1, 1, 1, 1]    cost = 12.0    try = 63
case = [1, 1, 1, 1, 1, 1]    cost = 0.0     try = 64

Best case(solution) = [1, 1, 0, 0, 1, 0]    cost = 33.0
In [25]:
draw_graph(G, colors_brute, pos)

QAOA solving Weighted Maxcut¶

In [26]:
from qiskit import QuantumCircuit, Aer
from qiskit.circuit import Parameter


def maxcut_obj(solution, graph):
    obj = 0
    for i, j in graph.edges():
        if solution[i] != solution[j]:
            obj -= 1 * w[i][j]
    return obj  # cost function(hamiltonian)


def compute_expectation(counts, graph):
    avg = 0
    sum_count = 0
    for bit_string, count in counts.items():
        obj = maxcut_obj(bit_string, graph)
        avg += obj * count
        sum_count += count  # sum_count is shot
    return avg/sum_count  # minimize this function


def create_qaoa_circ(graph, theta):
    nqubits = len(graph.nodes())
    n_layers = len(theta)//2
    beta = theta[:n_layers]
    gamma = theta[n_layers:]

    qc = QuantumCircuit(nqubits)

    qc.h(range(nqubits))

    for layer_index in range(n_layers):
        for pair in list(graph.edges()):
            qc.rzz(2 * gamma[layer_index] * w[pair[0]]
                   [pair[1]], pair[0], pair[1])
        for qubit in range(nqubits):
            qc.rx(2 * beta[layer_index], qubit)

    qc.measure_all()
    return qc


def get_expectation(graph, shots=512):
    backend = Aer.get_backend('qasm_simulator')
    backend.shots = shots

    def execute_circ(theta):
        qc = create_qaoa_circ(graph, theta)
        counts = backend.run(qc, seed_simulator=10,
                             nshots=512).result().get_counts()
        return compute_expectation(counts, graph)

    return execute_circ
In [27]:
from scipy.optimize import minimize
expectation = get_expectation(G)
p = 1  # 32 64
res = minimize(expectation, np.ones(p*2)*np.pi/2,
               method='COBYLA', options={'maxiter': 2500})
In [28]:
res
Out[28]:
     fun: -24.17529296875
   maxcv: 0.0
 message: 'Optimization terminated successfully.'
    nfev: 31
  status: 1
 success: True
       x: array([2.57910398, 1.5991255 ])
In [29]:
from qiskit.visualization import plot_histogram
backend = Aer.get_backend('aer_simulator')
backend.shots = 2**14

qc_res = create_qaoa_circ(G, res.x)
counts = backend.run(qc_res, seed_simulator=10).result().get_counts()
plot_histogram(counts, figsize=(20, 5), title='512 Shots')
Out[29]:
In [30]:
# Plot the Quantum Circuit of QAOA
# qc_res.draw(output='mpl', plot_barriers=True).savefig('QAOA_circuit.png', dpi=720)
qc_res.draw(output='mpl', plot_barriers=True)
Out[30]:
In [31]:
# qc_res.draw(output='mpl', plot_barriers=True, fold=-1).savefig('QAOA_circuit(full).png', dpi=720)
qc_res.draw(output='mpl', plot_barriers=True, fold=-1)
Out[31]:
In [32]:
str(counts)
Out[32]:
"{'001001': 54, '100001': 23, '001010': 15, '111111': 3, '101001': 79, '111010': 82, '001000': 16, '101000': 30, '011011': 22, '011110': 27, '000001': 2, '110110': 67, '010111': 23, '101100': 1, '000011': 6, '011111': 8, '110010': 16, '101110': 2, '000101': 67, '010001': 5, '001110': 4, '111011': 21, '100101': 65, '010110': 75, '110011': 3, '000100': 16, '101101': 8, '000111': 8, '100100': 25, '111100': 5, '001101': 34, '010010': 9, '101111': 5, '000110': 4, '110001': 13, '011010': 62, '100000': 8, '000000': 6, '110111': 12, '001100': 2, '100011': 12, '100111': 13, '011000': 9, '111000': 6, '000010': 3, '110101': 16, '101011': 2, '111001': 10, '010000': 5, '001011': 1, '111110': 3, '010011': 4, '010100': 1, '011100': 5, '010101': 1}"
In [33]:
# Sort the counted shot results
{k: v for k, v in sorted(counts.items(), key=lambda item: item[1])}
Out[33]:
{'101100': 1,
 '001011': 1,
 '010100': 1,
 '010101': 1,
 '000001': 2,
 '101110': 2,
 '001100': 2,
 '101011': 2,
 '111111': 3,
 '110011': 3,
 '000010': 3,
 '111110': 3,
 '001110': 4,
 '000110': 4,
 '010011': 4,
 '010001': 5,
 '111100': 5,
 '101111': 5,
 '010000': 5,
 '011100': 5,
 '000011': 6,
 '000000': 6,
 '111000': 6,
 '011111': 8,
 '101101': 8,
 '000111': 8,
 '100000': 8,
 '010010': 9,
 '011000': 9,
 '111001': 10,
 '110111': 12,
 '100011': 12,
 '110001': 13,
 '100111': 13,
 '001010': 15,
 '001000': 16,
 '110010': 16,
 '000100': 16,
 '110101': 16,
 '111011': 21,
 '011011': 22,
 '100001': 23,
 '010111': 23,
 '100100': 25,
 '011110': 27,
 '101000': 30,
 '001101': 34,
 '001001': 54,
 '011010': 62,
 '100101': 65,
 '110110': 67,
 '000101': 67,
 '010110': 75,
 '101001': 79,
 '111010': 82}
In [34]:
result_col = list(map(int, list(max(counts, key=counts.get))))
result_colors = ['g' if result_col[i] == 0 else 'c' for i in range(n)]
In [35]:
# Result of Brute Force algorithm
draw_graph(G, colors_brute, pos)
In [36]:
# Result of QAOA
draw_graph(G, result_colors, pos)
In [37]:
print('xbest_brute :', xbest_brute)
print('QAOA        :', result_col)

xbest_brute : [1, 1, 0, 0, 1, 0]
QAOA        : [1, 1, 1, 0, 1, 0]
In [ ]:

Simulating with Different P-Values¶

  • p is just an iteration number, where we perform repetative works and trying to find the best solution out of iteratively executed results.
In [38]:
from tqdm import tqdm

p = 16
res = []
for i in tqdm(range(1, p+1)):
    res.append(minimize(expectation, np.ones(i*2)*np.pi/2,
               method='COBYLA', options={'maxiter': 2500}))

100%|██████████| 16/16 [00:21<00:00,  1.31s/it]
In [39]:
res[0:2]
Out[39]:
[     fun: -24.17529296875
    maxcv: 0.0
  message: 'Optimization terminated successfully.'
     nfev: 31
   status: 1
  success: True
        x: array([2.57910398, 1.5991255 ]),
      fun: -24.716796875
    maxcv: 0.0
  message: 'Optimization terminated successfully.'
     nfev: 54
   status: 1
  success: True
        x: array([2.52461869, 1.63875349, 1.61624568, 1.52923708])]
In [40]:
approx = []
for i in range(p):
    approx.append(-res[i].fun/best_cost_brute)

x = np.arange(1, p+1, 1)

plt.figure(figsize=(8, 6))
plt.plot(x, approx, marker='o', markersize=6, c='k', linestyle='--')
plt.ylim((0.5, 1))
plt.xlim(0, p)
plt.xlabel('iteration')
plt.ylabel('Approximation')
plt.grid(True)
plt.show()
In [41]:
best_p = np.argmax(approx)
print("The best p(iterationo number) is", best_p)

The best p(iterationo number) is 11
  • When p=25, cost hamiltonian is optimized. So we use the best optimized values to output our results.
In [42]:
res[best_p].x
Out[42]:
array([2.69931677, 1.70145888, 1.83501131, 1.52640593, 1.70235575,
       1.52533461, 1.53010659, 1.94876412, 1.40228443, 1.54544357,
       1.47815615, 1.48456692, 1.58893494, 1.57102304, 1.58103879,
       1.68907833, 1.40984573, 1.6220806 , 1.63468791, 1.62148146,
       1.52878007, 1.70463034, 1.58593247, 1.60855217])
In [43]:
from qiskit.visualization import plot_histogram
backend = Aer.get_backend('aer_simulator')
backend.shots = 512

qc_res = create_qaoa_circ(G, res[best_p].x)
counts = backend.run(qc_res, seed_simulator=10).result().get_counts()
plot_histogram(counts, figsize=(20, 5), title='512 Shots')
Out[43]:
In [44]:
result_col = list(map(int, list(max(counts, key=counts.get))))
result_colors = ['g' if result_col[i] == 0 else 'c' for i in range(n)]
In [45]:
print('xbest_brute :', xbest_brute)
print('QAOA        :', result_col)

xbest_brute : [1, 1, 0, 0, 1, 0]
QAOA        : [1, 1, 0, 0, 1, 0]
In [46]:
draw_graph(G, colors_brute, pos)
In [47]:
draw_graph(G, result_colors, pos)
In [48]:
print('Best solution - Brute Force : ' +
      str(xbest_brute) + ',  cost = ' + str(best_cost_brute))
print('Best solution - QAOA        : ' + str(result_col) +
      ',  cost = ' + str(-res[best_p].fun))

Best solution - Brute Force : [1, 1, 0, 0, 1, 0],  cost = 33.0
Best solution - QAOA        : [1, 1, 0, 0, 1, 0],  cost = 28.9130859375
In [ ]:

Clustering using QAOA-Weighted Maxcut with Iris Data¶

In [49]:
data_iris
Out[49]:
sepal length (cm) sepal width (cm) petal length (cm) petal width (cm) species Euclid_dist Euclid_dist_sq
0 5.1 3.5 1.4 0.2 setosa 6.345077 40.26
1 4.9 3.0 1.4 0.2 setosa 5.916925 35.01
2 4.7 3.2 1.3 0.2 setosa 5.836095 34.06
3 4.6 3.1 1.5 0.2 setosa 5.749783 33.06
4 5.0 3.6 1.4 0.2 setosa 6.321392 39.96
... ... ... ... ... ... ... ...
145 6.7 3.0 5.2 2.3 virginica 9.285473 86.22
146 6.3 2.5 5.0 1.9 virginica 8.634234 74.55
147 6.5 3.0 5.2 2.0 virginica 9.071384 82.29
148 6.2 3.4 5.4 2.3 virginica 9.189668 84.45
149 5.9 3.0 5.1 1.8 virginica 8.547514 73.06

150 rows × 7 columns

  • Selected 3 datapoint of each from the different labels, total of 9 datapoints
In [50]:
num_sample1 = 6
num_sample2 = 6

sample_df1 = data_iris[data_iris['species'] ==
                       'setosa'].sample(num_sample1).sort_index()
# sample_df2 = data_iris[data_iris['species'] =='versicolor'].sample(num_sample).sort_index()
sample_df3 = data_iris[data_iris['species'] ==
                       'virginica'].sample(num_sample2).sort_index()

# data_iris_sample = pd.concat([sample_df1, sample_df2, sample_df3])
data_iris_sample = pd.concat([sample_df1, sample_df3])
data_iris_sample
Out[50]:
sepal length (cm) sepal width (cm) petal length (cm) petal width (cm) species Euclid_dist Euclid_dist_sq
8 4.4 2.9 1.4 0.2 setosa 5.456189 29.77
14 5.8 4.0 1.2 0.2 setosa 7.149825 51.12
15 5.7 4.4 1.5 0.4 setosa 7.366139 54.26
27 5.2 3.5 1.5 0.2 setosa 6.448256 41.58
33 5.5 4.2 1.4 0.2 setosa 7.063285 49.89
35 5.0 3.2 1.2 0.2 setosa 6.059703 36.72
114 5.8 2.8 5.1 2.4 virginica 8.558621 73.25
117 7.7 3.8 6.7 2.2 virginica 11.111256 123.46
125 7.2 3.2 6.0 1.8 virginica 10.065784 101.32
126 6.2 2.8 4.8 1.8 virginica 8.518216 72.56
140 6.7 3.1 5.6 2.4 virginica 9.571834 91.62
141 6.9 3.1 5.1 2.3 virginica 9.408507 88.52
In [51]:
data_iris_qaoa = data_iris_sample[[
    'sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']]
data_iris_qaoa = np.array(data_iris_qaoa)
data_iris_qaoa_label = iris.target[data_iris_sample.index]
In [52]:
data_iris_qaoa
Out[52]:
array([[4.4, 2.9, 1.4, 0.2],
       [5.8, 4. , 1.2, 0.2],
       [5.7, 4.4, 1.5, 0.4],
       [5.2, 3.5, 1.5, 0.2],
       [5.5, 4.2, 1.4, 0.2],
       [5. , 3.2, 1.2, 0.2],
       [5.8, 2.8, 5.1, 2.4],
       [7.7, 3.8, 6.7, 2.2],
       [7.2, 3.2, 6. , 1.8],
       [6.2, 2.8, 4.8, 1.8],
       [6.7, 3.1, 5.6, 2.4],
       [6.9, 3.1, 5.1, 2.3]])
In [53]:
data_iris_qaoa_label
Out[53]:
array([0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2])
In [54]:
len(data_iris_qaoa_label)
Out[54]:
12

Method 1: Brute Force Algorithms to Calculate Optimal Solution¶

In [55]:
# Function to calculate the distance between given two data points

import math


def dist(a, b):
    "Euclidean dist between two lists"
    d = np.linalg.norm(np.array(a) - np.array(b), axis=0)
    return round(d, 4)
In [56]:
import random

# Assign the number of nodes, edge connection, and its weight of the Graph.
n = len(data_iris_qaoa_label)
data = data_iris_qaoa
label = data_iris_qaoa_label

datapoints = data.tolist()
print("Data points:", datapoints)
labels = label
print("Data labels:", labels)

G = nx.Graph()
G.add_nodes_from(np.arange(0, n, 1))
for i in range(n):
    for j in range(n):
        if i > j:
            G.add_edge(i, j, weight=dist(datapoints[i], datapoints[j]))

colors = ['g' for node in G.nodes()]
pos = nx.spring_layout(G)

Data points: [[4.4, 2.9, 1.4, 0.2], [5.8, 4.0, 1.2, 0.2], [5.7, 4.4, 1.5, 0.4], [5.2, 3.5, 1.5, 0.2], [5.5, 4.2, 1.4, 0.2], [5.0, 3.2, 1.2, 0.2], [5.8, 2.8, 5.1, 2.4], [7.7, 3.8, 6.7, 2.2], [7.2, 3.2, 6.0, 1.8], [6.2, 2.8, 4.8, 1.8], [6.7, 3.1, 5.6, 2.4], [6.9, 3.1, 5.1, 2.3]]
Data labels: [0 0 0 0 0 0 2 2 2 2 2 2]
In [57]:
draw_graph(G, colors, pos)
In [58]:
# Calculate Adjacency matrix of the given Graph
w = np.zeros([n, n])
for i in range(n):
    for j in range(n):
        temp = G.get_edge_data(i, j, default=0)
        if temp != 0:
            w[i, j] = temp['weight']

w
Out[58]:
array([[0.    , 1.7916, 1.9975, 1.005 , 1.7029, 0.7   , 4.5277, 6.6174,
        5.6258, 4.1677, 5.2735, 4.9386],
       [1.7916, 0.    , 0.5477, 0.8367, 0.4123, 1.1314, 4.6357, 6.1563,
        5.3104, 4.1376, 5.0813, 4.6519],
       [1.9975, 0.5477, 0.    , 1.0488, 0.3606, 1.4353, 4.4193, 5.8856,
        5.0892, 3.9573, 4.8477, 4.4385],
       [1.005 , 0.8367, 1.0488, 0.    , 0.7681, 0.469 , 4.3186, 6.1139,
        5.1865, 3.8652, 4.9051, 4.5188],
       [1.7029, 0.4123, 0.3606, 0.7681, 0.    , 1.1358, 4.5365, 6.0902,
        5.2545, 4.0706, 5.013 , 4.6119],
       [0.7   , 1.1314, 1.4353, 0.469 , 1.1358, 0.    , 4.5662, 6.473 ,
        5.5172, 4.1376, 5.2058, 4.8208],
       [4.5277, 4.6357, 4.4193, 4.3186, 4.5365, 4.5662, 0.    , 2.6851,
        1.8138, 0.781 , 1.0724, 1.1446],
       [6.6174, 6.1563, 5.8856, 6.1139, 6.0902, 6.473 , 2.6851, 0.    ,
        1.1225, 2.6495, 1.6553, 1.9235],
       [5.6258, 5.3104, 5.0892, 5.1865, 5.2545, 5.5172, 1.8138, 1.1225,
        0.    , 1.6125, 0.8832, 1.077 ],
       [4.1677, 4.1376, 3.9573, 3.8652, 4.0706, 4.1376, 0.781 , 2.6495,
        1.6125, 0.    , 1.1576, 0.9592],
       [5.2735, 5.0813, 4.8477, 4.9051, 5.013 , 5.2058, 1.0724, 1.6553,
        0.8832, 1.1576, 0.    , 0.5477],
       [4.9386, 4.6519, 4.4385, 4.5188, 4.6119, 4.8208, 1.1446, 1.9235,
        1.077 , 0.9592, 0.5477, 0.    ]])
  • Brute Force Algorithm
In [59]:
best_cost_brute = 0
for b in range(2**n):
    x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]
    cost = 0
    for i in range(n):
        for j in range(n):
            cost = cost + w[i, j] * x[i] * (1-x[j])
    if best_cost_brute < cost:
        best_cost_brute = cost
        xbest_brute = x
    print('case =', '%-30s' % str(x), ' cost =', '%-24s' %
          str(cost), 'try =', str(b+1))

colors_brute = ['g' if xbest_brute[i] == 0 else 'c' for i in range(n)]
print('\nBest case(solution) =', '%-30s' %
      str(xbest_brute), ' cost =', '%-24s' % str(best_cost_brute))

case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 0.0                      try = 1
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 38.3477                  try = 2
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 34.692899999999995       try = 3
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 69.4574                  try = 4
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 34.027499999999996       try = 5
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 68.3802                  try = 6
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 67.625                   try = 7
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 98.39450000000004        try = 8
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 33.035700000000006       try = 9
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 69.3734                  try = 10
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 66.0552                  try = 11
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 98.8097                  try = 12
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 64.9656                  try = 13
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 97.3083                  try = 14
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 96.88969999999999        try = 15
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]  cost = 125.64920000000004       try = 16
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 33.956399999999995       try = 17
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 68.89830000000002        try = 18
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 67.82469999999999        try = 19
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 99.18340000000003        try = 20
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 67.2627                  try = 21
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 98.20960000000002        try = 22
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 100.03560000000002       try = 23
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 127.39930000000004       try = 24
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 65.4559                  try = 25
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 98.38780000000003        try = 26
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 97.65080000000003        try = 27
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 126.99950000000001       try = 28
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 96.66460000000001        try = 29
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 125.60150000000002       try = 30
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 127.76410000000001       try = 31
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]  cost = 153.11780000000005       try = 32
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 35.592099999999995       try = 33
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 72.53980000000001        try = 34
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 68.02220000000001        try = 35
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 101.3867                 try = 36
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 66.74900000000001        try = 37
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 99.7017                  try = 38
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 98.08370000000001        try = 39
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 127.45320000000002       try = 40
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 67.68980000000002        try = 41
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 102.62750000000001       try = 42
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 98.4465                  try = 43
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 129.80100000000002       try = 44
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 96.74910000000001        try = 45
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 127.69180000000001       try = 46
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 126.41040000000001       try = 47
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0]  cost = 153.76990000000004       try = 48
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 67.27690000000001        try = 49
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 100.8188                 try = 50
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 98.88239999999999        try = 51
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 128.8411                 try = 52
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 97.7126                  try = 53
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 127.25950000000003       try = 54
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 128.2227                 try = 55
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 154.18640000000002       try = 56
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 97.83840000000001        try = 57
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 129.37030000000001       try = 58
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 127.77050000000001       try = 59
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 155.71920000000003       try = 60
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 126.17650000000002       try = 61
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 153.7134                 try = 62
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 155.0132                 try = 63
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 178.96690000000007       try = 64
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 34.500899999999994       try = 65
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 63.793200000000006       try = 66
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 59.9224                  try = 67
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 85.63150000000002        try = 68
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 59.6898                  try = 69
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 84.9871                  try = 70
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 84.0159                  try = 71
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 105.73000000000003       try = 72
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 58.89940000000001        try = 73
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 86.1817                  try = 74
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 82.64750000000001        try = 75
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 106.3466                 try = 76
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 81.99070000000002        try = 77
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 105.278                  try = 78
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 104.6434                 try = 79
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0]  cost = 124.34750000000001       try = 80
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 59.3843                  try = 81
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 85.2708                  try = 82
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 83.98120000000002        try = 83
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 106.2845                 try = 84
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 83.85200000000002        try = 85
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 105.74350000000001       try = 86
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 107.3535                 try = 87
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 125.66180000000004       try = 88
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 82.24660000000002        try = 89
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 106.12310000000004       try = 90
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 105.1701                 try = 91
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 125.46340000000002       try = 92
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 104.61670000000002       try = 93
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 124.49820000000003       try = 94
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 126.44480000000001       try = 95
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0]  cost = 142.7431                 try = 96
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 60.9606                  try = 97
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 88.85290000000002        try = 98
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 84.11930000000002        try = 99
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 108.42840000000002       try = 100
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 83.27890000000002        try = 101
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 107.17620000000002       try = 102
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 105.34220000000003       try = 103
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 125.65630000000003       try = 104
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 84.42110000000001        try = 105
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 110.30340000000002       try = 106
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 105.90640000000003       try = 107
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 128.20550000000003       try = 108
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 104.64180000000002       try = 109
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 126.52910000000003       try = 110
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 125.03170000000003       try = 111
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0]  cost = 143.33579999999998       try = 112
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 83.57240000000002        try = 113
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 108.05890000000002       try = 114
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 105.90650000000002       try = 115
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 126.80980000000002       try = 116
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 105.16950000000003       try = 117
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 125.66100000000003       try = 118
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 126.40820000000002       try = 119
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 143.31650000000002       try = 120
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 105.4967                 try = 121
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 127.97320000000005       try = 122
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 126.15740000000002       try = 123
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 145.05069999999998       try = 124
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 124.99620000000003       try = 125
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 143.47769999999997       try = 126
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 144.5615                 try = 127
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]  cost = 159.4598                 try = 128
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 47.3723                  try = 129
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 72.4852                  try = 130
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 69.7526                  try = 131
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 91.2823                  try = 132
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 69.6286                  try = 133
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 90.7465                  try = 134
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 90.9135                  try = 135
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 108.44820000000001       try = 136
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 68.18020000000001        try = 137
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 91.2831                  try = 138
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 88.8871                  try = 139
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 108.40679999999999       try = 140
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 88.33890000000001        try = 141
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 107.44680000000001       try = 142
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 107.95040000000002       try = 143
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0]  cost = 123.47510000000001       try = 144
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 69.14829999999999        try = 145
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 90.85540000000002        try = 146
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 90.70400000000001        try = 147
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 108.82790000000001       try = 148
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 90.6834                  try = 149
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 108.39550000000001       try = 150
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 111.14370000000002       try = 151
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 125.27260000000004       try = 152
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 88.42                    try = 153
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 108.11710000000002       try = 154
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 108.30230000000002       try = 155
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 124.41620000000002       try = 156
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 107.85750000000003       try = 157
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 123.55960000000003       try = 158
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 126.64440000000002       try = 159
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0]  cost = 138.76330000000002       try = 160
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 70.0184                  try = 161
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 93.7313                  try = 162
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 90.1359                  try = 163
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 110.2656                 try = 164
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 89.40410000000001        try = 165
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 109.12200000000001       try = 166
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 108.42620000000002       try = 167
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 124.56090000000002       try = 168
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 89.8883                  try = 169
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 111.59120000000001       try = 170
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 108.33240000000002       try = 171
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 126.4521                 try = 172
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 107.17640000000003       try = 173
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 124.88430000000001       try = 174
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 124.52510000000001       try = 175
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0]  cost = 138.64980000000003       try = 176
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 89.5228                  try = 177
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 109.82990000000001       try = 178
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 108.81570000000002       try = 179
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 125.53960000000002       try = 180
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 108.18730000000002       try = 181
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 124.49940000000004       try = 182
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 126.38480000000001       try = 183
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 139.11370000000002       try = 184
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 107.85650000000003       try = 185
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 126.15360000000003       try = 186
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 125.47600000000003       try = 187
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 140.18990000000002       try = 188
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 124.42340000000004       try = 189
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 138.7255                 try = 190
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 140.94750000000002       try = 191
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0]  cost = 151.66640000000004       try = 192
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 76.50300000000001        try = 193
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 92.5605                  try = 194
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 89.6119                  try = 195
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 102.08619999999999       try = 196
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 89.92070000000001        try = 197
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 101.98320000000001       try = 198
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 101.93420000000002       try = 199
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 110.4135                 try = 200
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 88.6737                  try = 201
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 102.7212                 try = 202
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 100.1092                 try = 203
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 110.5735                 try = 204
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 99.99380000000001        try = 205
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 110.0463                 try = 206
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 110.33390000000001       try = 207
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0]  cost = 116.80319999999999       try = 208
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 89.206                   try = 209
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 101.85770000000001       try = 210
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 101.4903                 try = 211
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 110.55879999999999       try = 212
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 101.9025                 try = 213
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 110.55920000000002       try = 214
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 113.09140000000001       try = 215
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 118.1649                 try = 216
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 99.8405                  try = 217
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 110.48220000000002       try = 218
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 110.4514                 try = 219
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 117.50989999999999       try = 220
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 110.4394                 try = 221
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 117.08610000000003       try = 222
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 119.95490000000004       try = 223
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]  cost = 123.0184                 try = 224
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 90.0167                  try = 225
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 104.67420000000001       try = 226
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 100.86280000000001       try = 227
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 111.93710000000002       try = 228
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 100.56380000000001       try = 229
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 111.22630000000004       try = 230
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 110.31450000000004       try = 231
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 117.39380000000003       try = 232
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 101.24940000000001       try = 233
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 113.89690000000003       try = 234
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 110.4221                 try = 235
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 119.4864                 try = 236
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 109.69890000000002       try = 237
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 118.35140000000003       try = 238
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 117.77620000000002       try = 239
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0]  cost = 122.84550000000002       try = 240
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 100.44810000000001       try = 241
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 111.69980000000002       try = 242
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 110.46960000000001       try = 243
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 118.13810000000001       try = 244
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 110.27400000000003       try = 245
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 117.53070000000002       try = 246
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 119.20010000000002       try = 247
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 122.87360000000004       try = 248
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 110.14460000000001       try = 249
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 119.38630000000002       try = 250
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 118.49270000000001       try = 251
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 124.15120000000002       try = 252
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 117.87290000000003       try = 253
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 123.11960000000003       try = 254
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 125.12560000000005       try = 255
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]  cost = 126.78910000000005       try = 256
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 38.492599999999996       try = 257
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 65.5887                  try = 258
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 62.5647                  try = 259
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 86.0776                  try = 260
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 62.34170000000001        try = 261
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 85.44280000000002        try = 262
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 85.31840000000001        try = 263
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 104.83630000000001       try = 264
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 61.155300000000004       try = 265
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 86.24140000000001        try = 266
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 83.55399999999999        try = 267
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 105.0569                 try = 268
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 82.90679999999999        try = 269
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 103.99790000000003       try = 270
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 104.21010000000003       try = 271
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0]  cost = 121.718                  try = 272
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 61.94                    try = 273
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 85.6303                  try = 274
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 85.1875                  try = 275
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 105.2946                 try = 276
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 85.0679                  try = 277
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 104.76320000000001       try = 278
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 107.22000000000001       try = 279
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 123.33210000000003       try = 280
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 83.0665                  try = 281
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 104.74680000000002       try = 282
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 104.64060000000002       try = 283
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 122.73770000000003       try = 284
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 104.09680000000002       try = 285
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 121.78210000000003       try = 286
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 124.57550000000002       try = 287
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0]  cost = 138.6776                 try = 288
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 63.0503                  try = 289
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 88.74640000000001        try = 290
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 84.85959999999999        try = 291
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 106.97250000000001       try = 292
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 84.02879999999998        try = 293
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 105.72990000000003       try = 294
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 104.74270000000003       try = 295
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 122.86059999999999       try = 296
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 84.77499999999999        try = 297
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 108.4611                 try = 298
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 104.91090000000001       try = 299
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 125.01380000000002       try = 300
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 103.65590000000002       try = 301
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 123.34700000000002       try = 302
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 122.6964                 try = 303
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0]  cost = 138.8043                 try = 304
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 84.22609999999999        try = 305
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 106.51640000000002       try = 306
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 105.21080000000002       try = 307
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 123.91789999999999       try = 308
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 104.48340000000002       try = 309
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 122.7787                 try = 310
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 124.3727                 try = 311
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 139.0848                 try = 312
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 104.41460000000002       try = 313
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 124.69490000000002       try = 314
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 123.72590000000001       try = 315
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 140.423                  try = 316
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 122.57430000000001       try = 317
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 138.8596                 try = 318
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 140.7902                 try = 319
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0]  cost = 153.4923                 try = 320
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 69.3659                  try = 321
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 87.4066                  try = 322
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 84.16659999999999        try = 323
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 98.6241                  try = 324
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 84.37640000000002        try = 325
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 98.4221                  try = 326
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 98.08170000000001        try = 327
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 108.54420000000002       try = 328
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 83.3914                  try = 329
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 99.4221                  try = 330
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 96.51870000000002        try = 331
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 108.96620000000001       try = 332
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 96.30430000000001        try = 333
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 108.34000000000003       try = 334
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 108.33620000000002       try = 335
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0]  cost = 116.7887                 try = 336
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 83.74029999999999        try = 337
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 98.3752                  try = 338
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 97.71640000000001        try = 339
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 108.7681                 try = 340
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 98.0296                  try = 341
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 108.66950000000001       try = 342
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 110.9103                 try = 343
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 117.96700000000003       try = 344
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 96.22960000000002        try = 345
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 108.85450000000002       try = 346
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 108.53229999999999       try = 347
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 117.57400000000001       try = 348
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 108.4213                 try = 349
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 117.05120000000002       try = 350
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 119.62860000000002       try = 351
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0]  cost = 124.67530000000002       try = 352
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 84.7912                  try = 353
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 101.43190000000001       try = 354
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 97.32910000000001        try = 355
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 110.38660000000002       try = 356
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 96.93110000000001        try = 357
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 109.57680000000002       try = 358
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 108.37360000000001       try = 359
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 117.43610000000001       try = 360
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 97.87870000000001        try = 361
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 112.50940000000003       try = 362
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 108.74320000000003       try = 363
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 119.79070000000002       try = 364
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 107.92100000000002       try = 365
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 118.55670000000003       try = 366
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 117.69010000000003       try = 367
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0]  cost = 124.74260000000001       try = 368
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 96.894                   try = 369
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 110.12890000000002       try = 370
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 108.60730000000002       try = 371
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 118.259                  try = 372
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 108.3127                 try = 373
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 117.55260000000001       try = 374
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 118.93060000000001       try = 375
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 124.58730000000001       try = 376
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 108.4453                 try = 377
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 119.67020000000002       try = 378
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 118.4852                 try = 379
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 126.12690000000002       try = 380
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 117.76640000000002       try = 381
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 124.99630000000003       try = 382
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 126.71090000000002       try = 383
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0]  cost = 130.35760000000002       try = 384
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 83.61989999999999        try = 385
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 97.48120000000002        try = 386
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 95.37939999999999        try = 387
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 105.65750000000001       try = 388
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 95.69779999999999        try = 389
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 105.56410000000001       try = 390
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 106.3619                 try = 391
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 112.645                  try = 392
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 94.05480000000001        try = 393
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 105.90610000000002       try = 394
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 104.1409                 try = 395
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 112.409                  try = 396
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 104.03510000000001       try = 397
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 111.89140000000002       try = 398
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 113.02579999999999       try = 399
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0]  cost = 117.29889999999999       try = 400
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 94.8869                  try = 401
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 105.34240000000001       try = 402
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 105.82180000000001       try = 403
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 112.69409999999999       try = 404
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 106.2436                 try = 405
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 112.70410000000001       try = 406
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 116.0831                 try = 407
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 118.96040000000002       try = 408
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 103.7856                 try = 409
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 112.23110000000001       try = 410
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 113.0471                 try = 411
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 117.90940000000002       try = 412
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 113.0447                 try = 413
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 117.49520000000003       try = 414
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 121.21080000000002       try = 415
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0]  cost = 122.07810000000003       try = 416
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 95.2316                  try = 417
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 107.69290000000002       try = 418
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 104.7283                 try = 419
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 113.60640000000002       try = 420
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 104.4389                 try = 421
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 112.90520000000002       try = 422
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 112.8402                 try = 423
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 117.72330000000001       try = 424
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 104.72850000000001       try = 425
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 115.17980000000001       try = 426
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 112.5518                 try = 427
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 119.4199                 try = 428
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 111.83820000000001       try = 429
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 118.29450000000001       try = 430
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 118.56610000000002       try = 431
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0]  cost = 121.43920000000001       try = 432
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 104.227                  try = 433
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 113.28250000000001       try = 434
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 112.89910000000002       try = 435
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 118.37140000000001       try = 436
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 112.7131                 try = 437
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 117.77360000000002       try = 438
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 120.28980000000001       try = 439
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 121.76710000000001       try = 440
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 112.1877                 try = 441
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 119.23320000000001       try = 442
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 119.1864                 try = 443
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 122.64870000000002       try = 444
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 118.57620000000001       try = 445
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 121.62670000000001       try = 446
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 124.47950000000002       try = 447
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0]  cost = 123.94680000000002       try = 448
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 109.12300000000002       try = 449
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 113.9289                 try = 450
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 111.6111                 try = 451
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 112.8338                 try = 452
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 112.3623                 try = 453
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 113.17320000000001       try = 454
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 113.755                  try = 455
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 110.9827                 try = 456
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 110.92070000000001       try = 457
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 113.7166                 try = 458
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 111.7354                 try = 459
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 110.94809999999998       try = 460
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 112.06240000000003       try = 461
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 110.86330000000001       try = 462
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 111.7817                 try = 463
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0]  cost = 106.99939999999998       try = 464
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 111.31700000000001       try = 465
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 112.7171                 try = 466
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 112.9805                 try = 467
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 110.7974                 try = 468
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 113.8351                 try = 469
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 111.2402                 try = 470
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 114.4032                 try = 471
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 108.2251                 try = 472
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 111.5785                 try = 473
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 110.96860000000001       try = 474
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 111.56860000000002       try = 475
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 107.3755                 try = 476
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 111.99900000000002       try = 477
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 107.39410000000001       try = 478
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 110.89370000000001       try = 479
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0]  cost = 102.7056                 try = 480
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 111.60229999999999       try = 481
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 115.00819999999999       try = 482
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 111.82759999999999       try = 483
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 111.65030000000002       try = 484
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 111.971                  try = 485
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 111.3819                 try = 486
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 111.10090000000002       try = 487
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 106.92859999999999       try = 488
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 112.46199999999999       try = 489
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 113.8579                 try = 490
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 111.0139                 try = 491
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 108.82659999999998       try = 492
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 110.73310000000001       try = 493
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 108.13400000000001       try = 494
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 108.18960000000001       try = 495
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0]  cost = 102.00730000000001       try = 496
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 111.5247                 try = 497
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 111.5248                 try = 498
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 110.92540000000001       try = 499
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 107.3423                 try = 500
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 111.1722                 try = 501
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 107.1773                 try = 502
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 109.4775                 try = 503
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 101.8994                 try = 504
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 110.8482                 try = 505
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 108.83830000000002       try = 506
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 108.57550000000002       try = 507
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 102.9824                 try = 508
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 108.39810000000001       try = 509
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 102.39320000000001       try = 510
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 105.03                   try = 511
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0]  cost = 95.4419                  try = 512
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 31.495799999999996       try = 513
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 61.508100000000006       try = 514
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 57.913500000000006       try = 515
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 84.3426                  try = 516
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 57.6087                  try = 517
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 83.62599999999999        try = 518
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 82.931                   try = 519
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 105.36510000000003       try = 520
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 56.8011                  try = 521
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 84.80340000000001        try = 522
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 81.5454                  try = 523
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 105.96450000000002       try = 524
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 80.81640000000002        try = 525
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 104.8237                 try = 526
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 104.4653                 try = 527
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0]  cost = 124.88940000000001       try = 528
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 57.311                   try = 529
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 83.91750000000002        try = 530
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 82.90410000000001        try = 531
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 105.9274                 try = 532
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 82.70270000000002        try = 533
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 105.31420000000001       try = 534
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 107.2004                 try = 535
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 126.22870000000003       try = 536
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 81.08010000000002        try = 537
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 105.67660000000004       try = 538
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 104.99980000000001       try = 539
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 126.01310000000002       try = 540
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 104.37420000000003       try = 541
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 124.97570000000002       try = 542
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 127.19850000000001       try = 543
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0]  cost = 144.2168                 try = 544
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 58.81269999999999        try = 545
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 87.42500000000003        try = 546
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 82.96760000000002        try = 547
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 107.99670000000002       try = 548
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 82.05500000000002        try = 549
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 106.6723                 try = 550
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 105.1145                 try = 551
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 126.1486                 try = 552
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 83.18000000000002        try = 553
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 109.7823                 try = 554
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 105.6615                 try = 555
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 128.6806                 try = 556
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 104.32470000000002       try = 557
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 126.93199999999999       try = 558
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 125.71079999999999       try = 559
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0]  cost = 144.73490000000004       try = 560
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 82.35630000000002        try = 561
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 107.56280000000001       try = 562
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 105.68660000000001       try = 563
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 127.3099                 try = 564
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 104.87740000000002       try = 565
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 126.08890000000001       try = 566
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 127.1123                 try = 567
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 144.7406                 try = 568
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 105.18740000000003       try = 569
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 128.38390000000004       try = 570
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 126.8443                 try = 571
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 146.45760000000004       try = 572
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 125.61090000000003       try = 573
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 144.81240000000003       try = 574
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 146.1724                 try = 575
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0]  cost = 161.79070000000004       try = 576
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 64.43469999999999        try = 577
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 85.3916                  try = 578
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 81.581                   try = 579
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 98.9547                  try = 580
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 81.709                   try = 581
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 98.6709                  try = 582
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 97.7599                  try = 583
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 111.1386                 try = 584
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 81.10279999999999        try = 585
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 100.04970000000002       try = 586
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 96.57570000000001        try = 587
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 111.93939999999999       try = 588
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 96.27950000000001        try = 589
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 111.23140000000001       try = 590
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 110.657                  try = 591
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0]  cost = 122.0257                 try = 592
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 81.17689999999999        try = 593
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 98.72800000000001        try = 594
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 97.49860000000001        try = 595
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 111.46650000000002       try = 596
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 97.73                    try = 597
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 111.28610000000003       try = 598
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 112.95630000000001       try = 599
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 122.92920000000002       try = 600
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 96.30880000000002        try = 601
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 111.84990000000002       try = 602
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 110.95710000000001       try = 603
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 122.91500000000003       try = 604
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 110.76430000000002       try = 605
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 122.31040000000002       try = 606
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 124.3172                 try = 607
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0]  cost = 132.28010000000003       try = 608
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 82.6192                  try = 609
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 102.17610000000002       try = 610
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 97.5027                  try = 611
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 113.47640000000001       try = 612
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 97.02290000000002        try = 613
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 112.58480000000002       try = 614
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 110.811                  try = 615
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 122.78970000000001       try = 616
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 98.34930000000003        try = 617
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 115.89620000000002       try = 618
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 111.5594                 try = 619
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 125.52310000000001       try = 620
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 110.65540000000001       try = 621
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 124.20730000000002       try = 622
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 122.77010000000001       try = 623
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0]  cost = 132.73880000000003       try = 624
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 97.08980000000001        try = 625
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 113.24090000000002       try = 626
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 111.14870000000002       try = 627
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 123.7166                 try = 628
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 110.77230000000002       try = 629
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 122.92840000000001       try = 630
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 123.73580000000001       try = 631
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 132.30870000000004       try = 632
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 111.28370000000001       try = 633
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 125.42480000000003       try = 634
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 123.6692                 try = 635
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 134.22710000000004       try = 636
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 122.86860000000001       try = 637
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 133.01470000000006       try = 638
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 134.1587                 try = 639
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0]  cost = 140.7216                 try = 640
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 73.5691                  try = 641
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 90.34660000000002        try = 642
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 87.67420000000001        try = 643
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 100.86850000000001       try = 644
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 87.91080000000001        try = 645
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 100.69330000000002       try = 646
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 100.9205                 try = 647
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 110.1198                 try = 648
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 86.64660000000002        try = 649
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 101.41410000000002       try = 650
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 99.0783                  try = 651
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 110.2626                 try = 652
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 98.89070000000001        try = 653
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 109.66320000000002       try = 654
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 110.22700000000002       try = 655
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0]  cost = 117.4163                 try = 656
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 87.2039                  try = 657
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 100.57560000000004       try = 658
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 100.48440000000001       try = 659
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 110.27290000000002       try = 660
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 100.82440000000001       try = 661
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 110.20110000000004       try = 662
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 113.00950000000002       try = 663
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 118.80300000000003       try = 664
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 98.74520000000001        try = 665
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 110.10690000000002       try = 666
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 110.35230000000001       try = 667
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 118.13080000000002       try = 668
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 110.26810000000003       try = 669
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 117.63480000000003       try = 670
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 120.77980000000004       try = 671
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0]  cost = 124.56330000000004       try = 672
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 87.94000000000001        try = 673
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 103.31750000000002       try = 674
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 99.7823                  try = 675
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 111.57660000000001       try = 676
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 99.4111                  try = 677
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 110.79360000000003       try = 678
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 110.15800000000003       try = 679
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 117.9573                 try = 680
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 100.07950000000001       try = 681
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 113.44700000000003       try = 682
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 110.24840000000002       try = 683
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 120.03269999999999       try = 684
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 109.45300000000003       try = 685
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 118.8255                 try = 686
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 118.5265                 try = 687
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0]  cost = 124.3158                 try = 688
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 99.30320000000002        try = 689
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 111.27490000000003       try = 690
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 110.32090000000002       try = 691
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 118.7094                 try = 692
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 110.05310000000003       try = 693
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 118.02980000000001       try = 694
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 119.97540000000001       try = 695
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 124.36890000000001       try = 696
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 109.90650000000002       try = 697
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 119.86820000000002       try = 698
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 119.25080000000001       try = 699
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 125.6293                 try = 700
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 118.5588                 try = 701
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 124.52550000000004       try = 702
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 126.80770000000003       try = 703
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0]  cost = 129.1912                 try = 704
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 101.13780000000003       try = 705
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 108.85990000000002       try = 706
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 105.97149999999999       try = 707
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 110.11040000000001       try = 708
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 106.6409                 try = 709
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 110.368                  try = 710
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 110.37920000000001       try = 711
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 110.52309999999999       try = 712
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 105.5781                 try = 713
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 111.2902                 try = 714
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 108.7384                 try = 715
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 110.86729999999999       try = 716
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 108.98360000000001       try = 717
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 110.7007                 try = 718
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 111.04849999999999       try = 719
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0]  cost = 109.18239999999999       try = 720
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 105.6996                 try = 721
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 110.0159                 try = 722
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 109.70870000000001       try = 723
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 110.44179999999999       try = 724
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 110.48150000000001       try = 725
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 110.8028                 try = 726
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 113.3952                 try = 727
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 110.13329999999999       try = 728
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 108.6037                 try = 729
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 110.91000000000001       try = 730
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 110.9394                 try = 731
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 109.6625                 try = 732
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 111.28800000000001       try = 733
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 109.59930000000001       try = 734
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 112.5283                 try = 735
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0]  cost = 107.25640000000001       try = 736
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 106.37630000000001       try = 737
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 112.6984                 try = 738
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 108.9472                 try = 739
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 111.6861                 try = 740
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 109.00880000000001       try = 741
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 111.3359                 try = 742
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 110.48430000000002       try = 743
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 109.2282                 try = 744
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 109.87859999999999       try = 745
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 114.1907                 try = 746
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 110.7761                 try = 747
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 111.505                  try = 748
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 110.41350000000001       try = 749
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 110.73060000000001       try = 750
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 110.21560000000001       try = 751
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0]  cost = 106.94949999999999       try = 752
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 108.66650000000001       try = 753
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 111.5828                 try = 754
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 110.4128                 try = 755
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 109.7459                 try = 756
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 110.57780000000001       try = 757
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 109.49910000000001       try = 758
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 111.2287                 try = 759
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 106.5668                 try = 760
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 110.63260000000001       try = 761
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 111.5389                 try = 762
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 110.70549999999999       try = 763
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 108.0286                 try = 764
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 110.44630000000001       try = 765
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 107.3576                 try = 766
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 109.4238                 try = 767
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0]  cost = 102.7519                 try = 768
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 66.76339999999999        try = 769
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 85.52410000000002        try = 770
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 82.56030000000003        try = 771
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 97.73780000000001        try = 772
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 82.69790000000003        try = 773
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 97.46360000000004        try = 774
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 97.39940000000003        try = 775
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 108.5819                 try = 776
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 81.69570000000002        try = 777
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 98.44640000000003        try = 778
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 95.81920000000001        try = 779
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 108.98670000000004       try = 780
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 95.53260000000002        try = 781
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 108.28830000000004       try = 782
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 108.56070000000003       try = 783
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0]  cost = 117.73320000000001       try = 784
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 82.06960000000002        try = 785
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 97.42450000000002        try = 786
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 97.04190000000001        try = 787
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 108.81360000000002       try = 788
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 97.28290000000003        try = 789
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 108.64280000000004       try = 790
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 111.15980000000002       try = 791
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 118.93650000000004       try = 792
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 95.46570000000001        try = 793
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 108.81060000000005       try = 794
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 108.76460000000003       try = 795
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 118.52630000000005       try = 796
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 108.58140000000003       try = 797
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 117.93130000000005       try = 798
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 120.78490000000004       try = 799
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0]  cost = 126.55160000000004       try = 800
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 83.04590000000002        try = 801
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 100.40660000000001       try = 802
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 96.58000000000001        try = 803
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 110.35750000000002       try = 804
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 96.10980000000002        try = 805
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 109.47550000000003       try = 806
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 108.54850000000002       try = 807
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 118.33099999999999       try = 808
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 97.0402                  try = 809
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 112.39090000000004       try = 810
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 108.90090000000002       try = 811
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 120.6684                 try = 812
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 108.00650000000002       try = 813
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 119.3622                 try = 814
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 118.7718                 try = 815
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0]  cost = 126.5443                 try = 816
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 96.08050000000001        try = 817
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 110.03540000000002       try = 818
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 108.79000000000002       try = 819
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 119.16170000000001       try = 820
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 108.42320000000002       try = 821
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 118.38310000000001       try = 822
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 120.0373                 try = 823
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 126.41400000000002       try = 824
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 108.53860000000003       try = 825
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 120.48350000000002       try = 826
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 119.5747                 try = 827
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 127.93640000000003       try = 828
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 118.78370000000001       try = 829
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 126.73360000000002       try = 830
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 128.72440000000003       try = 831
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0]  cost = 133.0911                 try = 832
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 96.07470000000002        try = 833
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 105.78000000000002       try = 834
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 102.6002                 try = 835
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 108.72230000000002       try = 836
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 103.17060000000002       try = 837
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 108.88090000000001       try = 838
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 108.60070000000002       try = 839
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 110.7278                 try = 840
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 102.36980000000001       try = 841
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 110.06510000000003       try = 842
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 107.22190000000002       try = 843
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 111.33400000000002       try = 844
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 107.36810000000003       try = 845
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 111.06840000000003       try = 846
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 111.12480000000001       try = 847
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0]  cost = 111.2419                 try = 848
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 102.30790000000002       try = 849
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 108.60740000000003       try = 850
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 108.00880000000001       try = 851
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 110.72510000000001       try = 852
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 108.68260000000001       try = 853
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 110.98710000000001       try = 854
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 113.2881                 try = 855
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 112.00940000000001       try = 856
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 107.06680000000003       try = 857
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 111.35630000000003       try = 858
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 111.09430000000002       try = 859
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 111.80060000000003       try = 860
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 111.34390000000002       try = 861
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 111.63840000000003       try = 862
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 114.27600000000001       try = 863
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0]  cost = 110.98730000000002       try = 864
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 103.22480000000002       try = 865
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 111.53010000000003       try = 866
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 107.48750000000003       try = 867
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 112.20960000000001       try = 868
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 107.45010000000002       try = 869
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 111.7604                 try = 870
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 110.61740000000002       try = 871
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 111.34450000000002       try = 872
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 108.5819                 try = 873
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 114.8772                 try = 874
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 111.17120000000003       try = 875
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 113.88330000000002       try = 876
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 110.70960000000001       try = 877
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 113.00990000000003       try = 878
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 112.20350000000002       try = 879
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0]  cost = 110.92060000000001       try = 880
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 107.18640000000002       try = 881
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 112.08590000000002       try = 882
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 110.62450000000003       try = 883
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 111.94080000000001       try = 884
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 110.69050000000001       try = 885
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 111.59500000000001       try = 886
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 113.0332                 try = 887
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 110.3545                 try = 888
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 111.00730000000001       try = 889
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 113.89680000000001       try = 890
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 112.77200000000002       try = 891
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 112.07830000000001       try = 892
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 112.41380000000001       try = 893
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 111.30830000000002       try = 894
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 113.08310000000002       try = 895
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0]  cost = 108.3944                 try = 896
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 106.59170000000002       try = 897
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 112.11760000000002       try = 898
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 110.076                  try = 899
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 112.01870000000002       try = 900
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 110.75500000000001       try = 901
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 112.28590000000001       try = 902
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 113.1439                 try = 903
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 111.0916                 try = 904
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 109.2962                 try = 905
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 112.81210000000004       try = 906
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 111.10710000000002       try = 907
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 111.03980000000003       try = 908
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 111.36190000000002       try = 909
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 110.88280000000003       try = 910
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 112.07740000000003       try = 911
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0]  cost = 108.0151                 try = 912
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 109.71750000000002       try = 913
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 111.83760000000004       try = 914
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 112.37720000000002       try = 915
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 110.91410000000002       try = 916
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 113.15960000000001       try = 917
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 111.28470000000003       try = 918
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 114.72390000000001       try = 919
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 109.26580000000001       try = 920
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 110.88580000000003       try = 921
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 110.99590000000003       try = 922
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 111.87210000000002       try = 923
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 108.39900000000002       try = 924
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 112.23030000000003       try = 925
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 108.34540000000003       try = 926
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 112.12120000000002       try = 927
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0]  cost = 104.65310000000002       try = 928
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 109.9282                 try = 929
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 114.05410000000003       try = 930
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 111.14970000000001       try = 931
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 111.6924                 try = 932
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 111.2209                 try = 933
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 111.3518                 try = 934
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 111.347                  try = 935
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 107.89470000000001       try = 936
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 111.69470000000003       try = 937
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 113.81060000000004       try = 938
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 111.24280000000002       try = 939
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 109.7755                 try = 940
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 110.88980000000002       try = 941
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 109.01070000000003       try = 942
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 109.3425                 try = 943
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0]  cost = 103.8802                 try = 944
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 110.78240000000002       try = 945
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 111.50250000000003       try = 946
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 111.17930000000001       try = 947
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 108.31620000000001       try = 948
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 111.35390000000001       try = 949
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 108.07900000000002       try = 950
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 110.6554                 try = 951
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 103.7973                 try = 952
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 111.01270000000001       try = 953
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 109.72280000000003       try = 954
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 109.73620000000003       try = 955
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 104.8631                 try = 956
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 109.48660000000002       try = 957
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 104.20170000000002       try = 958
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 107.1147                 try = 959
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0]  cost = 98.24660000000002        try = 960
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 130.53280000000004       try = 961
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 127.00330000000002       try = 962
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 124.74570000000001       try = 963
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 117.63300000000002       try = 964
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 125.85750000000002       try = 965
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 118.33300000000003       try = 966
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 118.97500000000001       try = 967
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 107.86730000000001       try = 968
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 124.60010000000001       try = 969
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 119.06060000000004       try = 970
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 117.1396                 try = 971
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 108.01690000000002       try = 972
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 117.82720000000002       try = 973
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 108.29270000000001       try = 974
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 109.2713                 try = 975
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0]  cost = 96.15360000000001        try = 976
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 124.58560000000001       try = 977
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 117.65030000000003       try = 978
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 117.9739                 try = 979
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 107.45540000000003       try = 980
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 119.18910000000001       try = 981
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 108.25880000000001       try = 982
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 111.482                  try = 983
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 96.96849999999999        try = 984
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 117.11670000000002       try = 985
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 108.17140000000002       try = 986
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 108.83160000000001       try = 987
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 96.30310000000001        try = 988
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 109.6226                 try = 989
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 96.68230000000003        try = 990
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 100.24210000000001       try = 991
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0]  cost = 83.71860000000001        try = 992
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 124.7369                 try = 993
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 119.80740000000002       try = 994
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 116.68700000000001       try = 995
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 108.17429999999999       try = 996
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 117.19100000000002       try = 997
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 108.2665                 try = 998
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 108.04570000000001       try = 999
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 95.53800000000001        try = 1000
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 117.86620000000002       try = 1001
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 110.92670000000001       try = 1002
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 108.14289999999998       try = 1003
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 97.6202                  try = 1004
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 108.2227                 try = 1005
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 97.28820000000002        try = 1006
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 97.40400000000001        try = 1007
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0]  cost = 82.88629999999999        try = 1008
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 116.5181                 try = 1009
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 108.18280000000001       try = 1010
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 107.6436                 try = 1011
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 95.72510000000001        try = 1012
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 108.251                  try = 1013
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 95.9207                  try = 1014
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 98.2811                  try = 1015
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 82.36759999999998        try = 1016
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 108.1112                 try = 1017
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 97.7659                  try = 1018
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 97.5633                  try = 1019
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 83.6348                  try = 1020
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 97.7465                  try = 1021
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 83.4062                  try = 1022
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 86.1032                  try = 1023
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0]  cost = 68.17969999999998        try = 1024
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 35.6426                  try = 1025
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 63.44329999999999        try = 1026
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 60.17289999999999        try = 1027
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 84.39040000000001        try = 1028
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 59.97469999999999        try = 1029
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 83.78039999999999        try = 1030
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 83.4096                  try = 1031
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 103.63210000000002       try = 1032
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 58.868100000000005       try = 1033
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 84.65880000000001        try = 1034
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 81.72500000000001        try = 1035
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 103.9325                 try = 1036
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 81.10260000000002        try = 1037
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 102.8983                 try = 1038
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 102.86410000000001       try = 1039
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0]  cost = 121.07660000000001       try = 1040
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 59.573                   try = 1041
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 83.9679                  try = 1042
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 83.27870000000001        try = 1043
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 104.0904                 try = 1044
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 83.18390000000002        try = 1045
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 103.58380000000001       try = 1046
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 105.79419999999999       try = 1047
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 122.61090000000003       try = 1048
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 81.26230000000001        try = 1049
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 103.64720000000001       try = 1050
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 103.2946                 try = 1051
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 122.09630000000003       try = 1052
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 102.77560000000003       try = 1053
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 121.1655                 try = 1054
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 123.7125                 try = 1055
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0]  cost = 138.5192                 try = 1056
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 60.82309999999999        try = 1057
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 87.22380000000003        try = 1058
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 83.09060000000002        try = 1059
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 105.90810000000003       try = 1060
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 82.28460000000003        try = 1061
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 104.69030000000004       try = 1062
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 103.45670000000004       try = 1063
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 122.27920000000003       try = 1064
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 83.11060000000002        try = 1065
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 107.50130000000003       try = 1066
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 103.70470000000005       try = 1067
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 124.51220000000002       try = 1068
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 102.47450000000003       try = 1069
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 122.87020000000001       try = 1070
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 121.9732                 try = 1071
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0]  cost = 138.78570000000002       try = 1072
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 82.48190000000002        try = 1073
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 105.47680000000003       try = 1074
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 103.92480000000003       try = 1075
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 123.33650000000002       try = 1076
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 103.22220000000003       try = 1077
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 122.2221                 try = 1078
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 123.56970000000001       try = 1079
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 138.9864                 try = 1080
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 103.23320000000002       try = 1081
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 124.21810000000002       try = 1082
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 123.00270000000002       try = 1083
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 140.40439999999998       try = 1084
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 121.87590000000002       try = 1085
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 138.86579999999998       try = 1086
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 140.54999999999998       try = 1087
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0]  cost = 153.95669999999998       try = 1088
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 67.99869999999999        try = 1089
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 86.744                   try = 1090
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 83.25760000000001        try = 1091
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 98.41970000000002        try = 1092
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 83.49220000000003        try = 1093
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 98.24250000000002        try = 1094
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 97.65570000000002        try = 1095
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 108.82280000000002       try = 1096
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 82.587                   try = 1097
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 99.32230000000003        try = 1098
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 96.17250000000003        try = 1099
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 109.32460000000002       try = 1100
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 95.98290000000001        try = 1101
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 108.7232                 try = 1102
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 108.473                  try = 1103
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0]  cost = 117.6301                 try = 1104
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 82.8561                  try = 1105
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 98.19560000000001        try = 1106
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 97.29040000000002        try = 1107
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 109.04670000000002       try = 1108
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 97.62840000000001        try = 1109
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 108.97290000000002       try = 1110
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 110.96730000000001       try = 1111
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 118.72860000000003       try = 1112
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 95.90820000000001        try = 1113
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 109.23770000000002       try = 1114
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 108.66910000000003       try = 1115
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 118.4154                 try = 1116
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 108.58290000000002       try = 1117
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 117.91740000000003       try = 1118
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 120.2484                 try = 1119
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0]  cost = 125.99969999999999       try = 1120
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 84.0468                  try = 1121
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 101.39210000000004       try = 1122
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 97.04290000000003        try = 1123
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 110.80500000000005       try = 1124
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 96.66970000000003        try = 1125
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 110.02000000000004       try = 1126
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 108.57040000000005       try = 1127
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 118.33750000000003       try = 1128
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 97.69710000000002        try = 1129
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 113.03240000000004       try = 1130
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 109.01980000000003       try = 1131
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 120.77190000000003       try = 1132
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 108.22240000000002       try = 1133
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 119.56270000000004       try = 1134
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 118.44970000000004       try = 1135
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0]  cost = 126.20680000000002       try = 1136
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 96.63260000000002        try = 1137
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 110.57210000000003       try = 1138
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 108.80410000000005       try = 1139
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 119.16040000000004       try = 1140
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 108.53430000000003       try = 1141
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 118.47880000000004       try = 1142
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 119.61040000000003       try = 1143
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 125.97170000000001       try = 1144
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 108.74670000000002       try = 1145
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 120.67620000000002       try = 1146
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 119.24480000000004       try = 1147
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 127.59110000000004       try = 1148
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 118.55080000000004       try = 1149
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 126.48530000000004       try = 1150
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 127.95350000000005       try = 1151
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0]  cost = 132.3048                 try = 1152
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 79.70430000000002        try = 1153
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 94.27020000000003        try = 1154
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 91.92200000000003        try = 1155
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 102.90470000000003       try = 1156
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 92.26520000000002        try = 1157
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 102.83610000000003       try = 1158
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 103.38750000000002       try = 1159
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 110.37520000000002       try = 1160
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 90.70200000000003        try = 1161
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 103.25790000000003       try = 1162
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 101.24630000000003       try = 1163
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 110.21900000000002       try = 1164
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 101.16530000000004       try = 1165
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 109.72620000000002       try = 1166
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 110.61420000000003       try = 1167
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0]  cost = 115.5919                 try = 1168
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 91.45430000000002        try = 1169
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 102.61440000000003       try = 1170
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 102.84740000000002       try = 1171
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 110.42430000000002       try = 1172
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 103.29400000000003       try = 1173
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 110.45910000000003       try = 1174
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 113.59170000000003       try = 1175
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 117.17360000000004       try = 1176
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 100.91580000000002       try = 1177
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 110.06590000000003       try = 1178
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 110.63550000000002       try = 1179
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 116.20240000000004       try = 1180
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 110.65790000000003       try = 1181
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 115.81300000000002       try = 1182
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 119.28220000000005       try = 1183
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0]  cost = 120.85410000000003       try = 1184
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 91.93880000000003        try = 1185
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 105.10470000000004       try = 1186
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 101.89370000000004       try = 1187
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 111.47640000000004       try = 1188
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 101.62910000000004       try = 1189
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 110.80000000000005       try = 1190
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 110.48860000000005       try = 1191
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 116.07630000000003       try = 1192
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 101.99850000000002       try = 1193
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 113.15440000000004       try = 1194
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 110.28000000000004       try = 1195
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 117.85270000000003       try = 1196
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 109.59120000000004       try = 1197
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 116.75210000000004       try = 1198
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 116.77730000000005       try = 1199
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0]  cost = 120.35500000000003       try = 1200
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 101.41720000000004       try = 1201
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 111.17730000000003       try = 1202
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 110.54750000000004       try = 1203
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 116.72440000000005       try = 1204
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 110.38630000000005       try = 1205
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 116.15140000000005       try = 1206
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 118.42120000000004       try = 1207
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 120.60310000000004       try = 1208
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 109.94070000000004       try = 1209
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 117.69080000000004       try = 1210
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 117.39760000000004       try = 1211
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 121.56450000000004       try = 1212
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 116.81220000000003       try = 1213
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 120.56730000000005       try = 1214
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 123.17370000000005       try = 1215
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0]  cost = 123.34560000000002       try = 1216
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 106.69020000000003       try = 1217
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 112.20070000000003       try = 1218
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 109.63650000000003       try = 1219
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 111.56380000000001       try = 1220
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 110.41250000000002       try = 1221
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 111.92800000000003       try = 1222
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 112.26340000000003       try = 1223
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 110.1957                 try = 1224
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 109.05070000000002       try = 1225
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 112.55120000000002       try = 1226
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 110.32360000000003       try = 1227
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 110.24090000000001       try = 1228
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 110.67540000000002       try = 1229
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 110.18090000000002       try = 1230
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 110.85290000000003       try = 1231
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0]  cost = 106.77520000000001       try = 1232
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 109.36720000000001       try = 1233
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 111.47190000000002       try = 1234
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 111.48890000000003       try = 1235
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 110.0104                 try = 1236
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 112.36830000000002       try = 1237
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 110.47800000000002       try = 1238
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 113.39460000000003       try = 1239
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 107.92110000000001       try = 1240
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 110.19150000000002       try = 1241
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 110.28620000000002       try = 1242
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 110.63980000000002       try = 1243
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 107.1513                 try = 1244
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 111.09500000000003       try = 1245
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 107.19470000000003       try = 1246
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 110.44790000000002       try = 1247
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0]  cost = 102.96440000000003       try = 1248
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 109.79230000000003       try = 1249
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 113.90280000000003       try = 1250
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 110.47580000000002       try = 1251
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 111.00310000000003       try = 1252
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 110.64400000000002       try = 1253
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 110.75950000000005       try = 1254
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 110.23210000000005       try = 1255
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 106.76440000000004       try = 1256
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 111.21480000000001       try = 1257
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 113.31530000000002       try = 1258
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 110.22490000000003       try = 1259
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 108.74220000000003       try = 1260
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 109.96890000000003       try = 1261
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 108.07440000000004       try = 1262
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 107.88360000000004       try = 1263
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0]  cost = 102.40590000000003       try = 1264
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 110.19770000000003       try = 1265
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 110.90240000000003       try = 1266
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 110.05660000000003       try = 1267
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 107.17810000000003       try = 1268
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 110.32820000000004       try = 1269
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 107.03790000000004       try = 1270
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 109.09170000000003       try = 1271
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 102.21820000000004       try = 1272
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 110.08400000000003       try = 1273
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 108.77870000000003       try = 1274
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 108.26950000000001       try = 1275
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 103.38100000000003       try = 1276
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 108.11690000000003       try = 1277
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 102.81660000000004       try = 1278
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 105.20700000000004       try = 1279
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0]  cost = 96.32350000000005        try = 1280
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 72.3688                  try = 1281
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 88.91790000000002        try = 1282
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 86.27830000000002        try = 1283
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 99.2442                  try = 1284
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 86.52250000000002        try = 1285
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 99.07660000000001        try = 1286
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 99.3366                  try = 1287
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 108.3075                 try = 1288
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 85.22130000000001        try = 1289
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 99.76040000000002        try = 1290
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 97.4574                  try = 1291
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 108.41330000000002       try = 1292
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 97.2774                  try = 1293
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 107.82150000000001       try = 1294
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 108.41810000000002       try = 1295
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0]  cost = 115.37900000000002       try = 1296
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 85.79020000000001        try = 1297
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 98.93350000000001        try = 1298
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 98.87510000000002        try = 1299
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 108.43520000000001       try = 1300
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 99.2227                  try = 1301
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 108.37100000000001       try = 1302
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 111.21220000000002       try = 1303
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 116.77730000000003       try = 1304
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 97.1065                  try = 1305
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 108.23980000000002       try = 1306
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 108.51800000000001       try = 1307
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 116.06810000000003       try = 1308
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 108.4414                 try = 1309
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 115.57970000000002       try = 1310
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 118.75750000000001       try = 1311
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0]  cost = 122.31260000000002       try = 1312
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 86.51490000000001        try = 1313
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 101.664                  try = 1314
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 98.16160000000002        try = 1315
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 109.72750000000003       try = 1316
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 97.798                   try = 1317
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 108.95210000000002       try = 1318
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 108.34930000000003       try = 1319
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 115.92020000000001       try = 1320
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 98.42940000000002        try = 1321
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 111.56850000000004       try = 1322
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 108.40270000000001       try = 1323
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 117.95860000000003       try = 1324
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 107.6149                 try = 1325
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 116.75900000000003       try = 1326
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 116.49280000000002       try = 1327
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0]  cost = 122.0537                 try = 1328
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 97.66470000000001        try = 1329
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 109.40800000000002       try = 1330
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 108.48680000000002       try = 1331
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 116.6469                 try = 1332
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 108.2266                 try = 1333
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 115.9749                 try = 1334
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 117.9533                 try = 1335
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 122.11840000000001       try = 1336
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 108.043                  try = 1337
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 117.77630000000002       try = 1338
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 117.19170000000001       try = 1339
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 123.3418                 try = 1340
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 116.50730000000001       try = 1341
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 122.24560000000002       try = 1342
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 124.56060000000002       try = 1343
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0]  cost = 126.71570000000001       try = 1344
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 101.0973                 try = 1345
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 108.59100000000001       try = 1346
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 105.73540000000001       try = 1347
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 109.64590000000001       try = 1348
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 106.4124                 try = 1349
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 109.9111                 try = 1350
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 109.95510000000003       try = 1351
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 109.8706                 try = 1352
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 105.31259999999999       try = 1353
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 110.7963                 try = 1354
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 108.27730000000001       try = 1355
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 110.17780000000002       try = 1356
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 108.53010000000002       try = 1357
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 110.01880000000003       try = 1358
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 110.39940000000003       try = 1359
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0]  cost = 108.3049                 try = 1360
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 105.4457                 try = 1361
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 109.53359999999999       try = 1362
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 109.2592                 try = 1363
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 109.7639                 try = 1364
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 110.03960000000001       try = 1365
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 110.13250000000001       try = 1366
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 112.7577                 try = 1367
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 109.26740000000001       try = 1368
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 108.12480000000001       try = 1369
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 110.20270000000002       try = 1370
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 110.26490000000003       try = 1371
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 108.75960000000002       try = 1372
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 110.62110000000001       try = 1373
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 108.70400000000002       try = 1374
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 111.66580000000002       try = 1375
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0]  cost = 106.16550000000001       try = 1376
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 106.11100000000002       try = 1377
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 112.20470000000002       try = 1378
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 108.48630000000003       try = 1379
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 110.99680000000002       try = 1380
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 108.5555                 try = 1381
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 110.65420000000002       try = 1382
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 109.83540000000002       try = 1383
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 108.35090000000001       try = 1384
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 109.38830000000002       try = 1385
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 113.47200000000002       try = 1386
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 110.09020000000004       try = 1387
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 110.59070000000001       try = 1388
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 109.73520000000002       try = 1389
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 109.82390000000002       try = 1390
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 109.34170000000003       try = 1391
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0]  cost = 105.84720000000003       try = 1392
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 108.1878                 try = 1393
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 110.87570000000002       try = 1394
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 109.73850000000002       try = 1395
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 108.84320000000001       try = 1396
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 109.9111                 try = 1397
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 108.60400000000001       try = 1398
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 110.36640000000001       try = 1399
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 105.47610000000003       try = 1400
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 109.92890000000001       try = 1401
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 110.60680000000002       try = 1402
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 109.80620000000002       try = 1403
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 106.90090000000002       try = 1404
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 109.55460000000001       try = 1405
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 106.23750000000003       try = 1406
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 108.33650000000003       try = 1407
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0]  cost = 101.43620000000003       try = 1408
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 114.18550000000002       try = 1409
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 117.49980000000001       try = 1410
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 115.78240000000002       try = 1411
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 115.51350000000004       try = 1412
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 116.56800000000001       try = 1413
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 115.88730000000002       try = 1414
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 117.0695                 try = 1415
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 112.80560000000001       try = 1416
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 114.81020000000001       try = 1417
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 116.11450000000004       try = 1418
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 114.73370000000003       try = 1419
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 112.45480000000002       try = 1420
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 115.09510000000003       try = 1421
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 112.40440000000002       try = 1422
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 113.92320000000004       try = 1423
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0]  cost = 107.6493                 try = 1424
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 115.4265                 try = 1425
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 115.33500000000001       try = 1426
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 116.1988                 try = 1427
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 112.52410000000002       try = 1428
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 117.0878                 try = 1429
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 113.00130000000003       try = 1430
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 116.7647                 try = 1431
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 109.09500000000001       try = 1432
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 114.515                  try = 1433
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 112.41350000000004       try = 1434
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 113.61390000000002       try = 1435
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 107.92920000000002       try = 1436
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 114.07870000000001       try = 1437
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 107.98220000000002       try = 1438
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 112.08220000000001       try = 1439
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0]  cost = 102.40250000000003       try = 1440
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 115.3856                 try = 1441
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 117.29990000000004       try = 1442
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 114.71970000000003       try = 1443
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 113.05080000000004       try = 1444
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 114.89750000000002       try = 1445
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 112.81680000000003       try = 1446
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 113.13620000000002       try = 1447
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 107.47230000000002       try = 1448
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 115.07230000000003       try = 1449
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 114.97660000000005       try = 1450
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 112.73300000000002       try = 1451
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 109.05410000000003       try = 1452
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 112.48660000000002       try = 1453
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 108.39590000000001       try = 1454
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 109.05190000000003       try = 1455
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0]  cost = 101.37800000000004       try = 1456
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 114.355                  try = 1457
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 112.86350000000003       try = 1458
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 112.86450000000002       try = 1459
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 107.78980000000003       try = 1460
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 113.14570000000002       try = 1461
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 107.65920000000001       try = 1462
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 110.55980000000001       try = 1463
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 101.49010000000003       try = 1464
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 112.50550000000003       try = 1465
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 109.00400000000002       try = 1466
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 109.34160000000003       try = 1467
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 102.25690000000003       try = 1468
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 109.19860000000001       try = 1469
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 101.70210000000004       try = 1470
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 104.93930000000003       try = 1471
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0]  cost = 93.85960000000003        try = 1472
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 137.54380000000003       try = 1473
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 131.80270000000002       try = 1474
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 129.8693                 try = 1475
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 120.54500000000003       try = 1476
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 131.0877                 try = 1477
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 121.3516                 try = 1478
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 122.3178                 try = 1479
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 108.99850000000002       try = 1480
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 129.5313                 try = 1481
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 121.78020000000002       try = 1482
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 120.18340000000003       try = 1483
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 108.84910000000004       try = 1484
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 120.97760000000002       try = 1485
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 109.23150000000003       try = 1486
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 110.53430000000003       try = 1487
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0]  cost = 95.20500000000003        try = 1488
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 129.7118                 try = 1489
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 120.56490000000001       try = 1490
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 121.21270000000001       try = 1491
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 108.48260000000002       try = 1492
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 122.53450000000001       try = 1493
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 109.3926                 try = 1494
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 112.94000000000001       try = 1495
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 96.2149                  try = 1496
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 120.1631                 try = 1497
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 109.00620000000002       try = 1498
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 109.99060000000001       try = 1499
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 95.25050000000002        try = 1500
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 110.8882                 try = 1501
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 95.73630000000001        try = 1502
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 99.62030000000001        try = 1503
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0]  cost = 80.88520000000001        try = 1504
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 129.6115                 try = 1505
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 122.47040000000004       try = 1506
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 119.6742                 try = 1507
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 108.94990000000004       try = 1508
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 120.2848                 try = 1509
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 109.14870000000002       try = 1510
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 109.2521                 try = 1511
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 94.53280000000004        try = 1512
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 120.66100000000002       try = 1513
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 111.50990000000002       try = 1514
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 109.05030000000001       try = 1515
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 96.31600000000003        try = 1516
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 109.2367                 try = 1517
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 96.09060000000002        try = 1518
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 96.5306                  try = 1519
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0]  cost = 79.80130000000003        try = 1520
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 119.5079                 try = 1521
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 108.96100000000003       try = 1522
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 108.74600000000001       try = 1523
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 94.61590000000002        try = 1524
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 109.46000000000001       try = 1525
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 94.9181                  try = 1526
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 97.6027                  try = 1527
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 79.4776                  try = 1528
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 109.02120000000001       try = 1529
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 96.46430000000001        try = 1530
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 96.58590000000001        try = 1531
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 80.44580000000002        try = 1532
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 96.87570000000001        try = 1533
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 80.3238                  try = 1534
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 83.345                   try = 1535
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0]  cost = 63.20989999999999        try = 1536
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 64.8232                  try = 1537
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 84.28850000000001        try = 1538
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 81.07830000000001        try = 1539
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 96.96040000000002        try = 1540
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 81.2407                  try = 1541
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 96.71100000000001        try = 1542
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 96.40040000000002        try = 1543
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 108.28750000000002       try = 1544
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 80.31830000000001        try = 1545
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 97.77360000000002        try = 1546
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 94.90000000000002        try = 1547
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 108.77210000000002       try = 1548
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 94.63820000000001        try = 1549
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 108.09850000000002       try = 1550
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 108.1245                 try = 1551
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0]  cost = 118.0016                 try = 1552
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 80.61240000000001        try = 1553
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 96.67190000000002        try = 1554
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 96.04290000000003        try = 1555
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 108.51920000000003       try = 1556
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 96.30870000000002        try = 1557
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 108.37320000000003       try = 1558
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 110.64380000000001       try = 1559
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 119.12510000000005       try = 1560
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 94.57130000000001        try = 1561
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 108.62080000000005       try = 1562
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 108.32840000000003       try = 1563
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 118.79470000000003       try = 1564
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 108.17000000000003       try = 1565
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 118.22450000000005       try = 1566
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 120.8317                 try = 1567
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0]  cost = 127.303                  try = 1568
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 81.72850000000003        try = 1569
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 99.79380000000002        try = 1570
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 95.72080000000003        try = 1571
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 110.20290000000004       try = 1572
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 95.27540000000002        try = 1573
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 109.34570000000004       try = 1574
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 108.17230000000002       try = 1575
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 118.6594                 try = 1576
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 96.2856                  try = 1577
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 112.34090000000005       try = 1578
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 108.60450000000003       try = 1579
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 121.07660000000001       try = 1580
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 107.73490000000002       try = 1581
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 119.79520000000002       try = 1582
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 118.95840000000003       try = 1583
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0]  cost = 127.43550000000002       try = 1584
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 95.24610000000001        try = 1585
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 109.90560000000004       try = 1586
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 108.41380000000002       try = 1587
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 119.49010000000003       try = 1588
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 108.07180000000002       try = 1589
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 118.73630000000001       try = 1590
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 120.14410000000001       try = 1591
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 127.22540000000001       try = 1592
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 108.26700000000002       try = 1593
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 120.91650000000003       try = 1594
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 119.76130000000002       try = 1595
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 128.82760000000002       try = 1596
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 118.99510000000002       try = 1597
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 127.64960000000004       try = 1598
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 129.394                  try = 1599
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0]  cost = 134.46529999999998       try = 1600
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 95.6173                  try = 1601
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 106.02720000000001       try = 1602
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 102.60100000000001       try = 1603
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 109.42770000000002       try = 1604
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 103.19620000000002       try = 1605
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 109.61110000000002       try = 1606
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 109.08450000000002       try = 1607
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 111.9162                 try = 1608
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 102.4752                 try = 1609
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 110.87510000000002       try = 1610
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 107.78550000000001       try = 1611
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 112.60220000000001       try = 1612
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 107.9565                 try = 1613
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 112.36140000000002       try = 1614
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 112.1714                 try = 1615
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0]  cost = 112.99309999999998       try = 1616
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 102.3335                 try = 1617
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 109.33760000000002       try = 1618
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 108.49260000000001       try = 1619
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 111.91350000000001       try = 1620
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 109.19120000000001       try = 1621
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 112.20030000000001       try = 1622
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 114.2549                 try = 1623
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 113.6808                 try = 1624
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 107.65520000000001       try = 1625
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 112.64930000000003       try = 1626
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 112.1409                 try = 1627
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 113.55180000000001       try = 1628
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 112.4153                 try = 1629
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 113.41440000000001       try = 1630
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 115.80560000000001       try = 1631
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0]  cost = 113.2215                 try = 1632
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 103.39020000000001       try = 1633
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 112.40010000000004       try = 1634
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 108.11110000000002       try = 1635
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 113.53780000000003       try = 1636
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 108.09850000000002       try = 1637
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 113.11340000000003       try = 1638
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 111.72400000000002       try = 1639
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 113.15570000000002       try = 1640
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 109.31010000000002       try = 1641
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 116.31000000000003       try = 1642
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 112.35760000000002       try = 1643
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 115.77430000000003       try = 1644
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 111.92080000000003       try = 1645
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 114.92570000000002       try = 1646
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 113.87290000000002       try = 1647
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0]  cost = 113.29460000000002       try = 1648
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 107.83480000000002       try = 1649
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 113.43890000000003       try = 1650
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 111.73110000000001       try = 1651
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 113.75200000000001       try = 1652
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 111.82190000000001       try = 1653
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 113.43100000000003       try = 1654
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 114.62280000000001       try = 1655
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 112.6487                 try = 1656
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 112.21849999999999       try = 1657
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 115.81260000000003       try = 1658
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 114.44140000000002       try = 1659
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 114.45230000000002       try = 1660
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 114.108                  try = 1661
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 113.70710000000003       try = 1662
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 115.23550000000002       try = 1663
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0]  cost = 111.25140000000002       try = 1664
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 103.58590000000002       try = 1665
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 109.81640000000003       try = 1666
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 107.52840000000002       try = 1667
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 110.17570000000003       try = 1668
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 108.23220000000002       try = 1669
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 110.46770000000004       try = 1670
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 111.07930000000002       try = 1671
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 109.73160000000001       try = 1672
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 106.85320000000002       try = 1673
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 111.07370000000004       try = 1674
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 109.12230000000002       try = 1675
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 109.75960000000002       try = 1676
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 109.40190000000003       try = 1677
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 109.62740000000004       try = 1678
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 110.57560000000001       try = 1679
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0]  cost = 107.21790000000001       try = 1680
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 107.19470000000003       try = 1681
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 110.01940000000005       try = 1682
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 110.31260000000003       try = 1683
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 109.55410000000002       try = 1684
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 111.11980000000003       try = 1685
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 109.94950000000003       try = 1686
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 113.14230000000002       try = 1687
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 108.38880000000002       try = 1688
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 108.92580000000001       try = 1689
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 109.74050000000004       try = 1690
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 110.37030000000003       try = 1691
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 107.60180000000003       try = 1692
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 110.75330000000002       try = 1693
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 107.57300000000004       try = 1694
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 111.10240000000002       try = 1695
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0]  cost = 104.33890000000002       try = 1696
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 107.54520000000004       try = 1697
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 112.37570000000005       try = 1698
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 109.22490000000003       try = 1699
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 110.47220000000003       try = 1700
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 109.32090000000002       try = 1701
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 110.15640000000003       try = 1702
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 109.90520000000004       try = 1703
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 107.15750000000003       try = 1704
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 109.87450000000003       try = 1705
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 112.69500000000004       try = 1706
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 109.88080000000002       try = 1707
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 109.11810000000003       try = 1708
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 109.55260000000003       try = 1709
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 108.37810000000003       try = 1710
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 108.46350000000004       try = 1711
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0]  cost = 103.70580000000002       try = 1712
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 108.88240000000002       try = 1713
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 110.30710000000005       try = 1714
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 109.73750000000004       try = 1715
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 107.57900000000004       try = 1716
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 109.93690000000004       try = 1717
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 107.36660000000003       try = 1718
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 109.69660000000003       try = 1719
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 103.54310000000004       try = 1720
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 109.67550000000003       try = 1721
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 109.09020000000002       try = 1722
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 108.85720000000002       try = 1723
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 104.68870000000003       try = 1724
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 108.63240000000003       try = 1725
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 104.05210000000002       try = 1726
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 106.71870000000003       try = 1727
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0]  cost = 98.55520000000003        try = 1728
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 129.0098                 try = 1729
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 126.18490000000003       try = 1730
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 123.68090000000001       try = 1731
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 117.27280000000003       try = 1732
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 124.81750000000001       try = 1733
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 117.99760000000003       try = 1734
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 118.39320000000001       try = 1735
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 107.99010000000003       try = 1736
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 123.63990000000001       try = 1737
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 118.80500000000002       try = 1738
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 116.6376                 try = 1739
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 108.21950000000002       try = 1740
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 117.35000000000001       try = 1741
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 108.52010000000003       try = 1742
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 109.2523                 try = 1743
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0]  cost = 96.83920000000002        try = 1744
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 123.54560000000002       try = 1745
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 117.31490000000004       try = 1746
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 117.39210000000001       try = 1747
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 107.57820000000002       try = 1748
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 118.63210000000002       try = 1749
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 108.40640000000002       try = 1750
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 111.38320000000002       try = 1751
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 97.57430000000001        try = 1752
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 116.63950000000001       try = 1753
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 108.39880000000002       try = 1754
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 108.8126                 try = 1755
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 96.98870000000002        try = 1756
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 109.62840000000001       try = 1757
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 97.39270000000002        try = 1758
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 100.7061                 try = 1759
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0]  cost = 84.88720000000002        try = 1760
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 123.83670000000002       try = 1761
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 119.61180000000003       try = 1762
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 116.24500000000002       try = 1763
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 108.43690000000002       try = 1764
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 116.77380000000002       try = 1765
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 108.55390000000003       try = 1766
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 108.08670000000002       try = 1767
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 96.28360000000002        try = 1768
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 117.52880000000002       try = 1769
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 111.29390000000002       try = 1770
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 108.2637                 try = 1771
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 98.44560000000001        try = 1772
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 108.3683                 try = 1773
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 98.13840000000002        try = 1774
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 98.00780000000002        try = 1775
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0]  cost = 84.19470000000001        try = 1776
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 116.10090000000001       try = 1777
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 108.47020000000002       try = 1778
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 107.68460000000002       try = 1779
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 96.47070000000002        try = 1780
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 108.31680000000001       try = 1781
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 96.69110000000002        try = 1782
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 98.80510000000002        try = 1783
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 83.59620000000001        try = 1784
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 108.25680000000001       try = 1785
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 98.6161                  try = 1786
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 98.1671                  try = 1787
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 84.9432                  try = 1788
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 98.3751                  try = 1789
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 84.7394                  try = 1790
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 87.19000000000001        try = 1791
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0]  cost = 69.97109999999999        try = 1792
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 98.3244                  try = 1793
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 106.53810000000003       try = 1794
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 103.95870000000004       try = 1795
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 108.58920000000003       try = 1796
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 104.56350000000003       try = 1797
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 108.78220000000005       try = 1798
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 109.10240000000003       try = 1799
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 109.73790000000002       try = 1800
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 103.44650000000001       try = 1801
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 109.65020000000003       try = 1802
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 107.40740000000002       try = 1803
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 110.02790000000002       try = 1804
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 107.58800000000002       try = 1805
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 109.79670000000002       try = 1806
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 110.45350000000002       try = 1807
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0]  cost = 109.079                  try = 1808
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 103.60460000000002       try = 1809
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 108.41250000000004       try = 1810
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 108.41430000000003       try = 1811
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 109.63900000000002       try = 1812
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 109.12250000000003       try = 1813
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 109.93540000000003       try = 1814
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 112.83680000000001       try = 1815
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 110.06650000000002       try = 1816
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 107.19050000000003       try = 1817
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 109.98840000000004       try = 1818
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 110.32680000000002       try = 1819
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 109.54150000000003       try = 1820
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 110.61080000000003       try = 1821
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 109.41370000000003       try = 1822
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 112.65170000000002       try = 1823
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0]  cost = 107.87140000000002       try = 1824
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 104.19530000000002       try = 1825
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 111.00900000000003       try = 1826
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 107.56680000000003       try = 1827
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 110.79730000000004       try = 1828
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 107.56380000000003       try = 1829
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 110.38250000000004       try = 1830
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 109.83990000000001       try = 1831
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 109.07540000000003       try = 1832
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 108.37940000000002       try = 1833
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 113.18310000000002       try = 1834
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 110.07750000000001       try = 1835
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 111.29800000000004       try = 1836
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 109.65030000000003       try = 1837
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 110.45900000000003       try = 1838
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 110.25300000000001       try = 1839
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0]  cost = 107.47850000000001       try = 1840
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 107.20390000000003       try = 1841
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 110.61180000000003       try = 1842
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 109.75080000000001       try = 1843
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 109.57550000000002       try = 1844
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 109.8512                 try = 1845
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 109.26410000000003       try = 1846
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 111.30270000000002       try = 1847
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 107.1324                 try = 1848
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 109.85180000000001       try = 1849
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 111.24970000000005       try = 1850
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 110.72530000000003       try = 1851
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 108.54                   try = 1852
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 110.40150000000003       try = 1853
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 107.80440000000002       try = 1854
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 110.17960000000001       try = 1855
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0]  cost = 103.9993                 try = 1856
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 125.49090000000002       try = 1857
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 124.64920000000002       try = 1858
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 121.8538                 try = 1859
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 117.42890000000003       try = 1860
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 122.89140000000002       try = 1861
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 118.05470000000004       try = 1862
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 118.15890000000002       try = 1863
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 109.73900000000002       try = 1864
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 121.9758                 try = 1865
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 119.12410000000003       try = 1866
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 116.66530000000002       try = 1867
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 110.23040000000002       try = 1868
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 117.2787                 try = 1869
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 110.43200000000002       try = 1870
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 110.87280000000001       try = 1871
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0]  cost = 100.4429                 try = 1872
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 121.69810000000001       try = 1873
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 117.45060000000002       try = 1874
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 117.23640000000002       try = 1875
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 109.40570000000002       try = 1876
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 118.37740000000001       try = 1877
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 110.13490000000002       try = 1878
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 112.8203                 try = 1879
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 100.9946                 try = 1880
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 116.64680000000001       try = 1881
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 110.38930000000002       try = 1882
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 110.51170000000002       try = 1883
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 100.67100000000002       try = 1884
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 111.22850000000001       try = 1885
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 100.97600000000001       try = 1886
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 103.998                  try = 1887
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0]  cost = 90.16230000000002        try = 1888
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 122.22940000000001       try = 1889
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 119.98770000000003       try = 1890
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 116.32950000000001       try = 1891
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 110.50460000000001       try = 1892
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 116.75930000000002       try = 1893
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 110.5226                 try = 1894
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 109.76400000000002       try = 1895
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 99.94410000000002        try = 1896
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 117.7763                 try = 1897
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 113.52460000000002       try = 1898
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 110.203                  try = 1899
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 102.36810000000001       try = 1900
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 110.2086                 try = 1901
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 101.96190000000001       try = 1902
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 101.53990000000002       try = 1903
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0]  cost = 89.71000000000002        try = 1904
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 116.165                  try = 1905
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 110.51750000000001       try = 1906
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 109.44050000000001       try = 1907
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 100.20980000000002       try = 1908
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 109.97370000000001       try = 1909
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 100.3312                 try = 1910
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 102.1538                 try = 1911
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 88.9281                  try = 1912
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 110.1757                 try = 1913
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 102.51820000000002       try = 1914
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 101.77780000000001       try = 1915
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 90.53710000000001        try = 1916
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 101.8868                 try = 1917
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 90.23430000000002        try = 1918
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 92.3935                  try = 1919
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0]  cost = 77.15780000000001        try = 1920
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 134.84210000000002       try = 1921
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 129.82100000000003       try = 1922
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 128.1638                 try = 1923
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 119.55950000000001       try = 1924
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 129.31                   try = 1925
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 120.29390000000002       try = 1926
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 121.53630000000003       try = 1927
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 108.93700000000001       try = 1928
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 127.73640000000002       try = 1929
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 120.70530000000002       try = 1930
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 119.38470000000001       try = 1931
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 108.77040000000004       try = 1932
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 120.1067                 try = 1933
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 109.08060000000003       try = 1934
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 110.65960000000001       try = 1935
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0]  cost = 96.05030000000002        try = 1936
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 127.94190000000002       try = 1937
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 119.51500000000003       try = 1938
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 120.43900000000001       try = 1939
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 108.42890000000003       try = 1940
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 121.68860000000001       try = 1941
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 109.26670000000001       try = 1942
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 113.0903                 try = 1943
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 97.08520000000001        try = 1944
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 119.30000000000001       try = 1945
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 108.86310000000003       try = 1946
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 110.12370000000001       try = 1947
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 96.10360000000003        try = 1948
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 110.9491                 try = 1949
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 96.51720000000002        try = 1950
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 100.6774                 try = 1951
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0]  cost = 82.6623                  try = 1952
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 127.76700000000002       try = 1953
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 121.34590000000001       try = 1954
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 118.8259                 try = 1955
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 108.82160000000002       try = 1956
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 119.36430000000001       try = 1957
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 108.94820000000003       try = 1958
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 109.32780000000001       try = 1959
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 95.32850000000002        try = 1960
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 119.72330000000001       try = 1961
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 111.29220000000004       try = 1962
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 109.10880000000003       try = 1963
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 97.09450000000002        try = 1964
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 109.22300000000003       try = 1965
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 96.79690000000002        try = 1966
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 97.51310000000001        try = 1967
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0]  cost = 81.50380000000001        try = 1968
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 118.59520000000002       try = 1969
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 108.76830000000002       try = 1970
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 108.82950000000001       try = 1971
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 95.41940000000002        try = 1972
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 109.4713                 try = 1973
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 95.64940000000001        try = 1974
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 98.6102                  try = 1975
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 81.20510000000002        try = 1976
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 109.01530000000001       try = 1977
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 97.17840000000002        try = 1978
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 97.5762                  try = 1979
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 82.15610000000001        try = 1980
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 97.7938                  try = 1981
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 81.9619                  try = 1982
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 85.2593                  try = 1983
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0]  cost = 65.8442                  try = 1984
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 156.63840000000005       try = 1985
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 142.56190000000004       try = 1986
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 140.6887                 try = 1987
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 123.02900000000002       try = 1988
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 142.26770000000002       try = 1989
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 124.19620000000002       try = 1990
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 125.22260000000001       try = 1991
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 103.56790000000001       try = 1992
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 140.8955                 try = 1993
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 124.80900000000003       try = 1994
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 123.2724                 try = 1995
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 103.60270000000001       try = 1996
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 124.42720000000001       try = 1997
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 104.34570000000002       try = 1998
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 105.7087                 try = 1999
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0]  cost = 82.04400000000001        try = 2000
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 140.6652                 try = 2001
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 123.18290000000002       try = 2002
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 123.89090000000002       try = 2003
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 102.8254                 try = 2004
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 125.5733                 try = 2005
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 104.096                  try = 2006
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 107.70360000000001       try = 2007
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 82.6431                  try = 2008
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 123.38610000000001       try = 2009
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 103.89380000000001       try = 2010
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 104.9384                 try = 2011
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 81.86290000000001        try = 2012
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 106.1966                 try = 2013
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 82.7093                  try = 2014
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 86.6535                  try = 2015
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0]  cost = 59.58299999999999        try = 2016
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 140.43089999999998       try = 2017
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 124.95440000000004       try = 2018
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 122.21840000000002       try = 2019
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 103.15870000000001       try = 2020
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 123.18960000000001       try = 2021
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 103.7181                 try = 2022
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 103.88170000000001       try = 2023
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 80.82700000000001        try = 2024
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 123.75000000000001       try = 2025
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 106.26350000000002       try = 2026
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 103.86410000000001       try = 2027
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 82.79440000000001        try = 2028
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 104.41109999999999       try = 2029
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 82.92960000000001        try = 2030
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 83.4298                  try = 2031
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0]  cost = 58.3651                  try = 2032
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 122.18610000000001       try = 2033
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 103.30380000000001       try = 2034
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 103.14899999999999       try = 2035
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 80.68350000000001        try = 2036
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 104.22359999999999       try = 2037
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 81.34630000000001        try = 2038
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 84.09110000000001        try = 2039
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 57.6306                  try = 2040
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 103.969                  try = 2041
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 83.07670000000002        try = 2042
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 83.2585                  try = 2043
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 58.782999999999994       try = 2044
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 83.9089                  try = 2045
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 59.02159999999999        try = 2046
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 62.102999999999994       try = 2047
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]  cost = 33.6325                  try = 2048
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 33.6325                  try = 2049
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 62.10299999999999        try = 2050
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 59.021599999999985       try = 2051
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 83.90890000000002        try = 2052
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 58.78299999999999        try = 2053
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 83.2585                  try = 2054
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 83.0767                  try = 2055
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 103.96900000000002       try = 2056
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 57.63059999999999        try = 2057
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 84.09110000000001        try = 2058
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 81.34630000000001        try = 2059
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 104.22360000000002       try = 2060
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 80.68350000000002        try = 2061
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 103.14900000000002       try = 2062
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 103.3038                 try = 2063
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1]  cost = 122.18610000000002       try = 2064
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 58.365099999999984       try = 2065
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 83.4298                  try = 2066
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 82.92960000000001        try = 2067
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 104.41110000000002       try = 2068
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 82.79440000000001        try = 2069
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 103.86410000000001       try = 2070
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 106.2635                 try = 2071
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 123.75000000000004       try = 2072
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 80.82700000000001        try = 2073
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 103.88170000000002       try = 2074
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 103.71809999999999       try = 2075
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 123.18960000000003       try = 2076
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 103.1587                 try = 2077
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 122.21840000000003       try = 2078
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 124.95440000000002       try = 2079
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1]  cost = 140.43089999999998       try = 2080
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 59.582999999999984       try = 2081
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 86.65350000000001        try = 2082
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 82.70930000000001        try = 2083
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 106.19660000000002       try = 2084
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 81.86290000000001        try = 2085
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 104.93840000000002       try = 2086
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 103.89380000000001       try = 2087
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 123.38610000000001       try = 2088
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 82.64310000000002        try = 2089
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 107.70360000000001       try = 2090
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 104.09600000000002       try = 2091
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 125.57330000000002       try = 2092
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 102.82540000000002       try = 2093
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 123.8909                 try = 2094
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 123.1829                 try = 2095
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1]  cost = 140.6652                 try = 2096
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 82.04400000000001        try = 2097
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 105.7087                 try = 2098
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 104.34570000000001       try = 2099
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 124.42719999999998       try = 2100
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 103.6027                 try = 2101
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 123.27239999999998       try = 2102
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 124.80899999999997       try = 2103
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 140.89550000000003       try = 2104
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 103.56790000000001       try = 2105
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 125.22260000000001       try = 2106
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 124.19619999999999       try = 2107
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 142.2677                 try = 2108
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 123.029                  try = 2109
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 140.6887                 try = 2110
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 142.56189999999998       try = 2111
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1]  cost = 156.63840000000002       try = 2112
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 65.84419999999999        try = 2113
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 85.25930000000001        try = 2114
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 81.96190000000003        try = 2115
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 97.79380000000003        try = 2116
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 82.15610000000002        try = 2117
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 97.57620000000003        try = 2118
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 97.17840000000002        try = 2119
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 109.01530000000002       try = 2120
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 81.20510000000002        try = 2121
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 98.61020000000003        try = 2122
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 95.64940000000003        try = 2123
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 109.47130000000003       try = 2124
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 95.41940000000002        try = 2125
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 108.82950000000004       try = 2126
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 108.76830000000002       try = 2127
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1]  cost = 118.59520000000002       try = 2128
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 81.50380000000001        try = 2129
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 97.51310000000002        try = 2130
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 96.79690000000002        try = 2131
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 109.22300000000003       try = 2132
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 97.09450000000001        try = 2133
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 109.10880000000003       try = 2134
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 111.29220000000002       try = 2135
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 119.72330000000002       try = 2136
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 95.32850000000002        try = 2137
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 109.32780000000005       try = 2138
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 108.94820000000001       try = 2139
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 119.36430000000006       try = 2140
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 108.82160000000002       try = 2141
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 118.82590000000002       try = 2142
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 121.34590000000003       try = 2143
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1]  cost = 127.76700000000002       try = 2144
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 82.66230000000002        try = 2145
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 100.67740000000003       try = 2146
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 96.51720000000003        try = 2147
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 110.94910000000003       try = 2148
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 96.10360000000001        try = 2149
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 110.12370000000003       try = 2150
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 108.86310000000002       try = 2151
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 119.30000000000003       try = 2152
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 97.08520000000003        try = 2153
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 113.09030000000004       try = 2154
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 109.26670000000001       try = 2155
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 121.68860000000002       try = 2156
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 108.42890000000001       try = 2157
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 120.43900000000004       try = 2158
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 119.51500000000003       try = 2159
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1]  cost = 127.94190000000003       try = 2160
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 96.05030000000002        try = 2161
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 110.65960000000001       try = 2162
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 109.0806                 try = 2163
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 120.10670000000003       try = 2164
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 108.77040000000001       try = 2165
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 119.38470000000002       try = 2166
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 120.70530000000002       try = 2167
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 127.73640000000002       try = 2168
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 108.937                  try = 2169
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 121.53630000000004       try = 2170
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 120.29390000000001       try = 2171
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 129.31000000000003       try = 2172
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 119.55950000000001       try = 2173
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 128.16380000000004       try = 2174
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 129.82100000000003       try = 2175
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1]  cost = 134.8421                 try = 2176
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 77.15780000000001        try = 2177
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 92.39350000000002        try = 2178
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 90.2343                  try = 2179
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 101.88680000000001       try = 2180
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 90.53710000000001        try = 2181
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 101.77780000000001       try = 2182
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 102.51820000000001       try = 2183
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 110.1757                 try = 2184
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 88.92810000000001        try = 2185
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 102.15380000000002       try = 2186
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 100.33120000000002       try = 2187
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 109.97370000000001       try = 2188
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 100.20980000000002       try = 2189
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 109.44050000000001       try = 2190
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 110.51750000000001       try = 2191
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1]  cost = 116.165                  try = 2192
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 89.71000000000001        try = 2193
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 101.5399                 try = 2194
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 101.9619                 try = 2195
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 110.2086                 try = 2196
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 102.3681                 try = 2197
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 110.203                  try = 2198
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 113.5246                 try = 2199
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 117.7763                 try = 2200
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 99.9441                  try = 2201
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 109.76400000000001       try = 2202
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 110.52260000000001       try = 2203
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 116.75930000000002       try = 2204
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 110.50460000000001       try = 2205
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 116.32950000000004       try = 2206
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 119.98770000000002       try = 2207
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1]  cost = 122.22940000000001       try = 2208
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 90.1623                  try = 2209
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 103.99800000000002       try = 2210
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 100.97600000000001       try = 2211
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 111.22850000000001       try = 2212
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 100.671                  try = 2213
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 110.51170000000002       try = 2214
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 110.38930000000002       try = 2215
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 116.6468                 try = 2216
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 100.9946                 try = 2217
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 112.82030000000002       try = 2218
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 110.13490000000002       try = 2219
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 118.3774                 try = 2220
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 109.40570000000001       try = 2221
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 117.23640000000002       try = 2222
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 117.45060000000001       try = 2223
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1]  cost = 121.6981                 try = 2224
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 100.44290000000001       try = 2225
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 110.8728                 try = 2226
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 110.432                  try = 2227
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 117.27869999999999       try = 2228
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 110.2304                 try = 2229
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 116.6653                 try = 2230
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 119.12409999999998       try = 2231
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 121.97579999999999       try = 2232
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 109.739                  try = 2233
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 118.1589                 try = 2234
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 118.0547                 try = 2235
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 122.8914                 try = 2236
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 117.4289                 try = 2237
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 121.85380000000002       try = 2238
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 124.64920000000001       try = 2239
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1]  cost = 125.49090000000001       try = 2240
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 103.99930000000002       try = 2241
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 110.17960000000002       try = 2242
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 107.80440000000002       try = 2243
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 110.40150000000001       try = 2244
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 108.54                   try = 2245
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 110.72530000000002       try = 2246
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 111.24970000000002       try = 2247
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 109.85180000000001       try = 2248
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 107.1324                 try = 2249
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 111.30270000000002       try = 2250
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 109.26410000000001       try = 2251
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 109.8512                 try = 2252
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 109.5755                 try = 2253
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 109.75080000000001       try = 2254
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 110.61180000000002       try = 2255
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1]  cost = 107.2039                 try = 2256
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 107.47850000000001       try = 2257
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 110.25300000000001       try = 2258
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 110.459                  try = 2259
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 109.6503                 try = 2260
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 111.298                  try = 2261
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 110.07750000000001       try = 2262
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 113.18310000000001       try = 2263
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 108.37940000000002       try = 2264
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 109.0754                 try = 2265
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 109.83990000000001       try = 2266
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 110.38250000000001       try = 2267
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 107.56380000000001       try = 2268
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 110.79730000000002       try = 2269
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 107.56680000000001       try = 2270
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 111.00900000000001       try = 2271
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1]  cost = 104.19530000000002       try = 2272
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 107.8714                 try = 2273
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 112.6517                 try = 2274
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 109.4137                 try = 2275
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 110.61080000000001       try = 2276
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 109.5415                 try = 2277
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 110.32680000000002       try = 2278
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 109.98840000000001       try = 2279
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 107.19050000000001       try = 2280
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 110.06649999999999       try = 2281
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 112.83680000000001       try = 2282
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 109.93540000000002       try = 2283
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 109.1225                 try = 2284
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 109.63900000000001       try = 2285
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 108.41430000000003       try = 2286
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 108.41250000000002       try = 2287
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1]  cost = 103.6046                 try = 2288
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 109.079                  try = 2289
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 110.4535                 try = 2290
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 109.79670000000002       try = 2291
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 107.58800000000001       try = 2292
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 110.0279                 try = 2293
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 107.40740000000001       try = 2294
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 109.6502                 try = 2295
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 103.44650000000001       try = 2296
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 109.73790000000001       try = 2297
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 109.1024                 try = 2298
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 108.78219999999999       try = 2299
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 104.56350000000002       try = 2300
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 108.5892                 try = 2301
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 103.95870000000001       try = 2302
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 106.5381                 try = 2303
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1]  cost = 98.32440000000003        try = 2304
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 69.97109999999999        try = 2305
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 87.19000000000003        try = 2306
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 84.73940000000002        try = 2307
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 98.37510000000002        try = 2308
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 84.94320000000002        try = 2309
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 98.16710000000003        try = 2310
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 98.61610000000002        try = 2311
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 108.2568                 try = 2312
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 83.59620000000002        try = 2313
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 98.80510000000002        try = 2314
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 96.6911                  try = 2315
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 108.31680000000003       try = 2316
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 96.47070000000001        try = 2317
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 107.68460000000003       try = 2318
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 108.47020000000002       try = 2319
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1]  cost = 116.10090000000002       try = 2320
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 84.19470000000001        try = 2321
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 98.00780000000002        try = 2322
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 98.1384                  try = 2323
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 108.36830000000002       try = 2324
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 98.4456                  try = 2325
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 108.26370000000001       try = 2326
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 111.29390000000001       try = 2327
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 117.52880000000002       try = 2328
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 96.2836                  try = 2329
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 108.08670000000002       try = 2330
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 108.55390000000001       try = 2331
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 116.77380000000004       try = 2332
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 108.43690000000001       try = 2333
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 116.24500000000003       try = 2334
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 119.61180000000003       try = 2335
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1]  cost = 123.83670000000002       try = 2336
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 84.88720000000002        try = 2337
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 100.70610000000002       try = 2338
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 97.39270000000002        try = 2339
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 109.62840000000001       try = 2340
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 96.9887                  try = 2341
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 108.8126                 try = 2342
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 108.39880000000002       try = 2343
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 116.63949999999998       try = 2344
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 97.57430000000001        try = 2345
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 111.38320000000002       try = 2346
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 108.40640000000002       try = 2347
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 118.63210000000002       try = 2348
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 107.5782                 try = 2349
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 117.39210000000003       try = 2350
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 117.31490000000002       try = 2351
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1]  cost = 123.54560000000002       try = 2352
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 96.8392                  try = 2353
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 109.2523                 try = 2354
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 108.5201                 try = 2355
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 117.35                   try = 2356
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 108.2195                 try = 2357
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 116.63759999999999       try = 2358
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 118.80499999999998       try = 2359
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 123.63989999999998       try = 2360
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 107.99010000000001       try = 2361
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 118.39320000000001       try = 2362
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 117.99759999999999       try = 2363
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 124.81750000000001       try = 2364
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 117.27279999999999       try = 2365
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 123.6809                 try = 2366
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 126.18490000000001       try = 2367
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1]  cost = 129.0098                 try = 2368
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 98.55520000000001        try = 2369
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 106.71870000000001       try = 2370
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 104.05210000000002       try = 2371
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 108.6324                 try = 2372
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 104.68870000000003       try = 2373
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 108.8572                 try = 2374
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 109.09020000000001       try = 2375
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 109.67550000000004       try = 2376
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 103.54310000000002       try = 2377
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 109.69660000000002       try = 2378
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 107.36660000000003       try = 2379
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 109.93690000000002       try = 2380
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 107.57900000000002       try = 2381
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 109.73750000000004       try = 2382
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 110.30710000000002       try = 2383
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1]  cost = 108.88240000000003       try = 2384
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 103.70580000000001       try = 2385
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 108.46350000000001       try = 2386
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 108.37810000000002       try = 2387
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 109.55260000000003       try = 2388
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 109.11810000000001       try = 2389
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 109.88080000000002       try = 2390
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 112.69500000000002       try = 2391
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 109.87450000000003       try = 2392
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 107.15750000000003       try = 2393
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 109.90520000000004       try = 2394
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 110.15640000000003       try = 2395
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 109.32090000000002       try = 2396
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 110.47220000000003       try = 2397
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 109.22490000000003       try = 2398
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 112.37570000000002       try = 2399
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1]  cost = 107.54520000000004       try = 2400
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 104.33890000000002       try = 2401
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 111.1024                 try = 2402
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 107.57300000000002       try = 2403
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 110.75330000000002       try = 2404
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 107.6018                 try = 2405
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 110.37030000000003       try = 2406
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 109.74050000000001       try = 2407
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 108.92580000000004       try = 2408
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 108.38880000000003       try = 2409
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 113.14230000000002       try = 2410
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 109.94950000000004       try = 2411
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 111.11980000000003       try = 2412
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 109.55410000000003       try = 2413
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 110.31260000000002       try = 2414
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 110.0194                 try = 2415
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1]  cost = 107.19470000000004       try = 2416
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 107.2179                 try = 2417
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 110.57560000000001       try = 2418
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 109.62740000000002       try = 2419
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 109.40190000000001       try = 2420
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 109.7596                 try = 2421
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 109.12230000000001       try = 2422
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 111.0737                 try = 2423
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 106.85320000000003       try = 2424
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 109.73160000000001       try = 2425
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 111.07930000000002       try = 2426
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 110.46770000000002       try = 2427
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 108.23220000000003       try = 2428
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 110.1757                 try = 2429
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 107.52840000000002       try = 2430
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 109.81640000000002       try = 2431
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1]  cost = 103.58590000000004       try = 2432
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 111.2514                 try = 2433
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 115.23550000000003       try = 2434
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 113.7071                 try = 2435
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 114.10800000000002       try = 2436
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 114.4523                 try = 2437
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 114.44140000000002       try = 2438
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 115.8126                 try = 2439
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 112.21850000000002       try = 2440
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 112.6487                 try = 2441
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 114.62280000000004       try = 2442
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 113.43100000000001       try = 2443
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 111.82190000000004       try = 2444
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 113.752                  try = 2445
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 111.73110000000003       try = 2446
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 113.43890000000002       try = 2447
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1]  cost = 107.83480000000002       try = 2448
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 113.29459999999999       try = 2449
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 113.8729                 try = 2450
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 114.92569999999999       try = 2451
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 111.92080000000001       try = 2452
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 115.77429999999998       try = 2453
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 112.3576                 try = 2454
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 116.30999999999999       try = 2455
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 109.31009999999999       try = 2456
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 113.1557                 try = 2457
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 111.72400000000003       try = 2458
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 113.1134                 try = 2459
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 108.09850000000003       try = 2460
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 113.5378                 try = 2461
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 108.11110000000001       try = 2462
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 112.40010000000001       try = 2463
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1]  cost = 103.39020000000002       try = 2464
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 113.22149999999999       try = 2465
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 115.80560000000001       try = 2466
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 113.41440000000001       try = 2467
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 112.4153                 try = 2468
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 113.55179999999999       try = 2469
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 112.1409                 try = 2470
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 112.6493                 try = 2471
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 107.65520000000001       try = 2472
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 113.6808                 try = 2473
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 114.2549                 try = 2474
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 112.20030000000001       try = 2475
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 109.19120000000001       try = 2476
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 111.9135                 try = 2477
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 108.4926                 try = 2478
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 109.3376                 try = 2479
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1]  cost = 102.33350000000002       try = 2480
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 112.99309999999998       try = 2481
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 112.1714                 try = 2482
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 112.3614                 try = 2483
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 107.95649999999999       try = 2484
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 112.6022                 try = 2485
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 107.7855                 try = 2486
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 110.87509999999999       try = 2487
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 102.47519999999999       try = 2488
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 111.9162                 try = 2489
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 109.08450000000002       try = 2490
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 109.61110000000001       try = 2491
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 103.1962                 try = 2492
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 109.42770000000002       try = 2493
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 102.601                  try = 2494
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 106.0272                 try = 2495
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1]  cost = 95.6173                  try = 2496
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 134.46529999999998       try = 2497
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 129.394                  try = 2498
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 127.6496                 try = 2499
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 118.99510000000001       try = 2500
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 128.82760000000002       try = 2501
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 119.76130000000002       try = 2502
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 120.9165                 try = 2503
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 108.26700000000002       try = 2504
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 127.22540000000004       try = 2505
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 120.14410000000002       try = 2506
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 118.73630000000004       try = 2507
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 108.07180000000002       try = 2508
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 119.49010000000004       try = 2509
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 108.41380000000002       try = 2510
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 109.9056                 try = 2511
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1]  cost = 95.24610000000001        try = 2512
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 127.4355                 try = 2513
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 118.95840000000001       try = 2514
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 119.79520000000001       try = 2515
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 107.73490000000001       try = 2516
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 121.0766                 try = 2517
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 108.6045                 try = 2518
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 112.3409                 try = 2519
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 96.2856                  try = 2520
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 118.6594                 try = 2521
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 108.17230000000002       try = 2522
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 109.34570000000001       try = 2523
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 95.27540000000002        try = 2524
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 110.2029                 try = 2525
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 95.72080000000003        try = 2526
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 99.7938                  try = 2527
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1]  cost = 81.72850000000001        try = 2528
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 127.30299999999998       try = 2529
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 120.83170000000001       try = 2530
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 118.2245                 try = 2531
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 108.17000000000003       try = 2532
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 118.79469999999999       try = 2533
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 108.32839999999999       try = 2534
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 108.6208                 try = 2535
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 94.57130000000002        try = 2536
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 119.12509999999999       try = 2537
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 110.64380000000003       try = 2538
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 108.3732                 try = 2539
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 96.3087                  try = 2540
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 108.5192                 try = 2541
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 96.04290000000003        try = 2542
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 96.6719                  try = 2543
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1]  cost = 80.61240000000002        try = 2544
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 118.00159999999998       try = 2545
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 108.12450000000001       try = 2546
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 108.0985                 try = 2547
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 94.63820000000001        try = 2548
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 108.77209999999998       try = 2549
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 94.89999999999999        try = 2550
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 97.77359999999999        try = 2551
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 80.3183                  try = 2552
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 108.2875                 try = 2553
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 96.4004                  try = 2554
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 96.711                   try = 2555
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 81.2407                  try = 2556
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 96.9604                  try = 2557
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 81.0783                  try = 2558
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 84.2885                  try = 2559
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1]  cost = 64.8232                  try = 2560
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 63.209899999999976       try = 2561
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 83.34500000000001        try = 2562
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 80.32380000000002        try = 2563
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 96.87570000000004        try = 2564
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 80.44580000000002        try = 2565
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 96.58590000000001        try = 2566
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 96.46430000000001        try = 2567
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 109.02120000000004       try = 2568
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 79.47760000000001        try = 2569
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 97.60270000000003        try = 2570
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 94.91810000000002        try = 2571
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 109.46000000000004       try = 2572
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 94.61590000000001        try = 2573
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 108.74600000000002       try = 2574
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 108.96100000000001       try = 2575
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1]  cost = 119.50790000000003       try = 2576
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 79.80130000000001        try = 2577
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 96.53060000000004        try = 2578
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 96.09060000000004        try = 2579
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 109.23670000000004       try = 2580
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 96.31600000000002        try = 2581
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 109.05030000000002       try = 2582
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 111.50990000000002       try = 2583
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 120.66100000000004       try = 2584
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 94.53280000000002        try = 2585
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 109.25210000000004       try = 2586
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 109.14870000000003       try = 2587
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 120.28480000000005       try = 2588
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 108.94990000000003       try = 2589
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 119.67420000000004       try = 2590
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 122.47040000000003       try = 2591
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1]  cost = 129.61150000000004       try = 2592
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 80.88520000000001        try = 2593
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 99.62030000000001        try = 2594
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 95.73630000000001        try = 2595
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 110.88820000000003       try = 2596
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 95.25050000000002        try = 2597
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 109.99060000000001       try = 2598
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 109.0062                 try = 2599
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 120.1631                 try = 2600
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 96.21490000000001        try = 2601
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 112.94000000000004       try = 2602
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 109.39260000000002       try = 2603
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 122.53450000000001       try = 2604
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 108.48260000000002       try = 2605
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 121.21270000000001       try = 2606
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 120.56490000000001       try = 2607
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1]  cost = 129.71179999999998       try = 2608
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 95.20500000000001        try = 2609
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 110.53430000000002       try = 2610
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 109.23150000000001       try = 2611
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 120.97760000000001       try = 2612
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 108.8491                 try = 2613
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 120.1834                 try = 2614
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 121.7802                 try = 2615
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 129.53130000000002       try = 2616
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 108.9985                 try = 2617
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 122.31780000000002       try = 2618
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 121.3516                 try = 2619
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 131.08769999999998       try = 2620
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 120.54500000000002       try = 2621
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 129.86929999999998       try = 2622
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 131.8027                 try = 2623
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1]  cost = 137.5438                 try = 2624
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 93.85960000000001        try = 2625
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 104.93930000000003       try = 2626
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 101.70210000000003       try = 2627
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 109.19860000000004       try = 2628
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 102.25690000000003       try = 2629
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 109.34160000000004       try = 2630
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 109.00400000000002       try = 2631
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 112.50550000000003       try = 2632
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 101.49010000000003       try = 2633
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 110.55980000000004       try = 2634
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 107.65920000000003       try = 2635
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 113.14570000000003       try = 2636
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 107.78980000000003       try = 2637
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 112.86450000000004       try = 2638
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 112.86350000000003       try = 2639
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1]  cost = 114.35500000000002       try = 2640
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 101.37800000000001       try = 2641
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 109.05190000000003       try = 2642
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 108.39590000000003       try = 2643
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 112.48660000000004       try = 2644
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 109.05410000000002       try = 2645
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 112.73300000000003       try = 2646
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 114.97660000000002       try = 2647
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 115.07230000000004       try = 2648
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 107.47230000000003       try = 2649
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 113.13620000000004       try = 2650
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 112.81680000000003       try = 2651
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 114.89750000000005       try = 2652
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 113.05080000000002       try = 2653
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 114.71970000000005       try = 2654
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 117.29990000000002       try = 2655
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1]  cost = 115.38560000000003       try = 2656
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 102.40250000000002       try = 2657
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 112.08220000000004       try = 2658
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 107.98220000000002       try = 2659
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 114.07870000000003       try = 2660
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 107.92920000000002       try = 2661
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 113.61390000000004       try = 2662
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 112.41350000000003       try = 2663
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 114.51500000000001       try = 2664
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 109.09500000000001       try = 2665
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 116.76470000000005       try = 2666
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 113.00130000000003       try = 2667
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 117.08780000000003       try = 2668
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 112.52410000000003       try = 2669
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 116.19880000000003       try = 2670
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 115.33500000000002       try = 2671
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1]  cost = 115.42650000000002       try = 2672
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 107.64930000000001       try = 2673
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 113.92320000000002       try = 2674
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 112.40440000000002       try = 2675
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 115.09510000000002       try = 2676
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 112.4548                 try = 2677
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 114.73370000000001       try = 2678
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 116.11450000000002       try = 2679
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 114.81020000000002       try = 2680
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 112.80560000000001       try = 2681
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 117.06950000000003       try = 2682
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 115.88730000000002       try = 2683
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 116.56800000000004       try = 2684
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 115.51350000000001       try = 2685
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 115.78240000000002       try = 2686
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 117.49980000000001       try = 2687
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1]  cost = 114.18550000000002       try = 2688
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 101.43620000000001       try = 2689
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 108.33650000000003       try = 2690
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 106.23750000000003       try = 2691
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 109.55460000000002       try = 2692
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 106.90090000000002       try = 2693
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 109.80620000000003       try = 2694
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 110.60680000000002       try = 2695
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 109.92890000000001       try = 2696
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 105.47610000000002       try = 2697
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 110.36640000000004       try = 2698
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 108.60400000000001       try = 2699
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 109.91110000000002       try = 2700
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 108.84320000000001       try = 2701
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 109.73850000000003       try = 2702
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 110.87570000000001       try = 2703
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1]  cost = 108.18780000000001       try = 2704
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 105.84720000000003       try = 2705
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 109.34170000000005       try = 2706
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 109.82390000000002       try = 2707
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 109.73520000000002       try = 2708
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 110.59070000000001       try = 2709
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 110.09020000000002       try = 2710
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 113.47200000000001       try = 2711
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 109.38830000000002       try = 2712
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 108.35090000000002       try = 2713
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 109.83540000000004       try = 2714
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 110.65420000000002       try = 2715
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 108.55550000000002       try = 2716
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 110.99680000000002       try = 2717
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 108.48630000000004       try = 2718
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 112.20470000000005       try = 2719
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1]  cost = 106.11100000000002       try = 2720
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 106.16550000000001       try = 2721
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 111.66580000000003       try = 2722
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 108.70400000000002       try = 2723
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 110.62110000000003       try = 2724
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 108.7596                 try = 2725
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 110.26490000000003       try = 2726
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 110.20270000000001       try = 2727
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 108.12480000000001       try = 2728
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 109.26740000000002       try = 2729
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 112.75770000000003       try = 2730
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 110.13250000000002       try = 2731
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 110.03960000000002       try = 2732
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 109.76390000000002       try = 2733
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 109.25920000000004       try = 2734
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 109.53360000000002       try = 2735
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1]  cost = 105.44569999999999       try = 2736
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 108.30490000000002       try = 2737
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 110.39940000000003       try = 2738
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 110.01880000000001       try = 2739
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 108.5301                 try = 2740
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 110.17780000000002       try = 2741
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 108.27730000000001       try = 2742
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 110.7963                 try = 2743
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 105.3126                 try = 2744
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 109.87060000000002       try = 2745
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 109.95510000000003       try = 2746
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 109.9111                 try = 2747
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 106.4124                 try = 2748
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 109.64590000000001       try = 2749
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 105.73540000000001       try = 2750
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 108.591                  try = 2751
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1]  cost = 101.0973                 try = 2752
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 126.71570000000003       try = 2753
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 124.56060000000004       try = 2754
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 122.24560000000001       try = 2755
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 116.50730000000003       try = 2756
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 123.3418                 try = 2757
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 117.19170000000004       try = 2758
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 117.7763                 try = 2759
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 108.04300000000003       try = 2760
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 122.11840000000002       try = 2761
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 117.95330000000004       try = 2762
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 115.9749                 try = 2763
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 108.22660000000002       try = 2764
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 116.64690000000002       try = 2765
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 108.48680000000003       try = 2766
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 109.408                  try = 2767
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1]  cost = 97.66470000000002        try = 2768
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 122.05370000000002       try = 2769
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 116.49280000000003       try = 2770
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 116.75900000000001       try = 2771
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 107.61490000000003       try = 2772
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 117.95860000000002       try = 2773
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 108.40270000000001       try = 2774
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 111.56850000000001       try = 2775
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 98.4294                  try = 2776
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 115.92020000000002       try = 2777
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 108.34930000000003       try = 2778
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 108.95210000000002       try = 2779
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 97.79800000000003        try = 2780
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 109.7275                 try = 2781
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 98.16160000000002        try = 2782
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 101.66400000000002       try = 2783
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1]  cost = 86.51490000000003        try = 2784
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 122.31260000000002       try = 2785
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 118.75750000000002       try = 2786
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 115.57970000000002       try = 2787
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 108.44140000000002       try = 2788
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 116.0681                 try = 2789
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 108.51800000000003       try = 2790
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 108.2398                 try = 2791
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 97.10650000000003        try = 2792
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 116.77730000000001       try = 2793
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 111.21220000000002       try = 2794
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 108.37100000000001       try = 2795
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 99.2227                  try = 2796
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 108.43520000000001       try = 2797
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 98.87510000000002        try = 2798
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 98.93350000000001        try = 2799
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1]  cost = 85.79020000000001        try = 2800
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 115.379                  try = 2801
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 108.41810000000001       try = 2802
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 107.82150000000001       try = 2803
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 97.27740000000001        try = 2804
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 108.4133                 try = 2805
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 97.45740000000002        try = 2806
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 99.7604                  try = 2807
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 85.2213                  try = 2808
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 108.30750000000002       try = 2809
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 99.3366                  try = 2810
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 99.07660000000001        try = 2811
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 86.5225                  try = 2812
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 99.2442                  try = 2813
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 86.27830000000002        try = 2814
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 88.91789999999999        try = 2815
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1]  cost = 72.3688                  try = 2816
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 96.32350000000001        try = 2817
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 105.20700000000005       try = 2818
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 102.81660000000005       try = 2819
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 108.11690000000004       try = 2820
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 103.38100000000004       try = 2821
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 108.26950000000005       try = 2822
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 108.77870000000004       try = 2823
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 110.08400000000005       try = 2824
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 102.21820000000004       try = 2825
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 109.09170000000005       try = 2826
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 107.03790000000004       try = 2827
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 110.32820000000005       try = 2828
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 107.17810000000004       try = 2829
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 110.05660000000005       try = 2830
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 110.90240000000003       try = 2831
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1]  cost = 110.19770000000004       try = 2832
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 102.40590000000003       try = 2833
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 107.88360000000004       try = 2834
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 108.07440000000004       try = 2835
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 109.96890000000005       try = 2836
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 108.74220000000003       try = 2837
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 110.22490000000003       try = 2838
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 113.31530000000002       try = 2839
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 111.21480000000004       try = 2840
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 106.76440000000004       try = 2841
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 110.23210000000006       try = 2842
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 110.75950000000005       try = 2843
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 110.64400000000006       try = 2844
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 111.00310000000003       try = 2845
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 110.47580000000005       try = 2846
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 113.90280000000003       try = 2847
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1]  cost = 109.79230000000005       try = 2848
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 102.96440000000003       try = 2849
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 110.44790000000003       try = 2850
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 107.19470000000003       try = 2851
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 111.09500000000003       try = 2852
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 107.15130000000002       try = 2853
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 110.63980000000004       try = 2854
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 110.28620000000002       try = 2855
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 110.19150000000002       try = 2856
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 107.92110000000002       try = 2857
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 113.39460000000004       try = 2858
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 110.47800000000004       try = 2859
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 112.36830000000002       try = 2860
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 110.01040000000003       try = 2861
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 111.48890000000004       try = 2862
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 111.4719                 try = 2863
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1]  cost = 109.36720000000001       try = 2864
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 106.77520000000003       try = 2865
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 110.85290000000003       try = 2866
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 110.18090000000002       try = 2867
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 110.67540000000002       try = 2868
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 110.24090000000001       try = 2869
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 110.32360000000003       try = 2870
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 112.55120000000001       try = 2871
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 109.0507                 try = 2872
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 110.19570000000003       try = 2873
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 112.26340000000005       try = 2874
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 111.92800000000003       try = 2875
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 110.41250000000002       try = 2876
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 111.56380000000003       try = 2877
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 109.63650000000001       try = 2878
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 112.2007                 try = 2879
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1]  cost = 106.69020000000002       try = 2880
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 123.34560000000003       try = 2881
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 123.17370000000007       try = 2882
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 120.56730000000003       try = 2883
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 116.81220000000006       try = 2884
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 121.56450000000004       try = 2885
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 117.39760000000005       try = 2886
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 117.69080000000004       try = 2887
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 109.94070000000004       try = 2888
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 120.60310000000004       try = 2889
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 118.42120000000006       try = 2890
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 116.15140000000004       try = 2891
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 110.38630000000003       try = 2892
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 116.72440000000005       try = 2893
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 110.54750000000004       try = 2894
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 111.17730000000005       try = 2895
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1]  cost = 101.41720000000004       try = 2896
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 120.35500000000003       try = 2897
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 116.77730000000005       try = 2898
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 116.75210000000004       try = 2899
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 109.59120000000004       try = 2900
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 117.85270000000003       try = 2901
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 110.28000000000004       try = 2902
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 113.15440000000002       try = 2903
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 101.99850000000004       try = 2904
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 116.07630000000005       try = 2905
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 110.48860000000006       try = 2906
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 110.80000000000004       try = 2907
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 101.62910000000005       try = 2908
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 111.47640000000004       try = 2909
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 101.89370000000004       try = 2910
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 105.10470000000004       try = 2911
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1]  cost = 91.93880000000004        try = 2912
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 120.85410000000003       try = 2913
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 119.28220000000003       try = 2914
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 115.81300000000002       try = 2915
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 110.65790000000003       try = 2916
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 116.20240000000001       try = 2917
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 110.63550000000002       try = 2918
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 110.06590000000003       try = 2919
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 100.91580000000003       try = 2920
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 117.17360000000004       try = 2921
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 113.59170000000003       try = 2922
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 110.45910000000005       try = 2923
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 103.29400000000004       try = 2924
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 110.42430000000003       try = 2925
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 102.84740000000005       try = 2926
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 102.61440000000003       try = 2927
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1]  cost = 91.45430000000002        try = 2928
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 115.59190000000002       try = 2929
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 110.61420000000003       try = 2930
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 109.72620000000003       try = 2931
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 101.16530000000003       try = 2932
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 110.21900000000002       try = 2933
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 101.24630000000003       try = 2934
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 103.2579                 try = 2935
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 90.70200000000003        try = 2936
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 110.37520000000004       try = 2937
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 103.38750000000003       try = 2938
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 102.83610000000003       try = 2939
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 92.26520000000004        try = 2940
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 102.90470000000002       try = 2941
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 91.92200000000004        try = 2942
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 94.27020000000002        try = 2943
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1]  cost = 79.70430000000003        try = 2944
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 132.30480000000003       try = 2945
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 127.95350000000005       try = 2946
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 126.48530000000001       try = 2947
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 118.55080000000004       try = 2948
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 127.59110000000003       try = 2949
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 119.24480000000003       try = 2950
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 120.67620000000001       try = 2951
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 108.74670000000003       try = 2952
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 125.97170000000003       try = 2953
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 119.61040000000004       try = 2954
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 118.47880000000004       try = 2955
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 108.53430000000004       try = 2956
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 119.16040000000004       try = 2957
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 108.80410000000005       try = 2958
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 110.5721                 try = 2959
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1]  cost = 96.63260000000002        try = 2960
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 126.20680000000002       try = 2961
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 118.44970000000004       try = 2962
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 119.5627                 try = 2963
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 108.22240000000002       try = 2964
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 120.7719                 try = 2965
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 109.01980000000002       try = 2966
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 113.03240000000001       try = 2967
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 97.69710000000002        try = 2968
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 118.33750000000002       try = 2969
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 108.57040000000003       try = 2970
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 110.02000000000002       try = 2971
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 96.66970000000003        try = 2972
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 110.80500000000002       try = 2973
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 97.04290000000003        try = 2974
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 101.39210000000001       try = 2975
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1]  cost = 84.04680000000002        try = 2976
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 125.99970000000003       try = 2977
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 120.24840000000003       try = 2978
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 117.9174                 try = 2979
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 108.58290000000002       try = 2980
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 118.41539999999999       try = 2981
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 108.66910000000001       try = 2982
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 109.2377                 try = 2983
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 95.90820000000002        try = 2984
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 118.72860000000003       try = 2985
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 110.96730000000004       try = 2986
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 108.97290000000001       try = 2987
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 97.62840000000004        try = 2988
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 109.04670000000002       try = 2989
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 97.29040000000002        try = 2990
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 98.19560000000001        try = 2991
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1]  cost = 82.85610000000001        try = 2992
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 117.63010000000001       try = 2993
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 108.47300000000001       try = 2994
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 108.72320000000002       try = 2995
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 95.98290000000001        try = 2996
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 109.3246                 try = 2997
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 96.1725                  try = 2998
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 99.32230000000001        try = 2999
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 82.58700000000002        try = 3000
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 108.82280000000003       try = 3001
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 97.65570000000002        try = 3002
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 98.24250000000002        try = 3003
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 83.49220000000001        try = 3004
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 98.41970000000002        try = 3005
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 83.25760000000001        try = 3006
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 86.744                   try = 3007
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1]  cost = 67.9987                  try = 3008
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 153.9567                 try = 3009
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 140.55                   try = 3010
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 138.8658                 try = 3011
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 121.87590000000004       try = 3012
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 140.4044                 try = 3013
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 123.00270000000005       try = 3014
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 124.21810000000002       try = 3015
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 103.23320000000004       try = 3016
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 138.9864                 try = 3017
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 123.56970000000007       try = 3018
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 122.22210000000003       try = 3019
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 103.22220000000004       try = 3020
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 123.33650000000004       try = 3021
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 103.92480000000003       try = 3022
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 105.47680000000001       try = 3023
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1]  cost = 82.48190000000004        try = 3024
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 138.7857                 try = 3025
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 121.97320000000003       try = 3026
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 122.87020000000001       try = 3027
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 102.47450000000003       try = 3028
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 124.5122                 try = 3029
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 103.70470000000002       try = 3030
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 107.50130000000001       try = 3031
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 83.11060000000003        try = 3032
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 122.27920000000003       try = 3033
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 103.45670000000004       try = 3034
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 104.69030000000002       try = 3035
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 82.28460000000003        try = 3036
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 105.9081                 try = 3037
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 83.09060000000002        try = 3038
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 87.22380000000001        try = 3039
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1]  cost = 60.823100000000004       try = 3040
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 138.51919999999998       try = 3041
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 123.71250000000002       try = 3042
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 121.16550000000001       try = 3043
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 102.77560000000001       try = 3044
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 122.09630000000001       try = 3045
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 103.29460000000002       try = 3046
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 103.64720000000003       try = 3047
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 81.26230000000002        try = 3048
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 122.61090000000003       try = 3049
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 105.79420000000002       try = 3050
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 103.58380000000004       try = 3051
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 83.18390000000002        try = 3052
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 104.09040000000003       try = 3053
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 83.27870000000003        try = 3054
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 83.96790000000001        try = 3055
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1]  cost = 59.57300000000001        try = 3056
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 121.07660000000001       try = 3057
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 102.86410000000002       try = 3058
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 102.8983                 try = 3059
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 81.10260000000002        try = 3060
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 103.9325                 try = 3061
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 81.72500000000002        try = 3062
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 84.6588                  try = 3063
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 58.868100000000005       try = 3064
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 103.63210000000001       try = 3065
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 83.40960000000001        try = 3066
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 83.7804                  try = 3067
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 59.9747                  try = 3068
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 84.3904                  try = 3069
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 60.1729                  try = 3070
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 63.443299999999994       try = 3071
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]  cost = 35.6426                  try = 3072
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 68.1797                  try = 3073
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 86.1032                  try = 3074
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 83.4062                  try = 3075
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 97.7465                  try = 3076
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 83.63480000000001        try = 3077
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 97.56329999999998        try = 3078
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 97.76589999999999        try = 3079
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 108.11120000000003       try = 3080
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 82.36760000000001        try = 3081
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 98.28110000000001        try = 3082
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 95.92070000000001        try = 3083
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 108.25100000000002       try = 3084
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 95.7251                  try = 3085
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 107.6436                 try = 3086
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 108.1828                 try = 3087
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1]  cost = 116.5181                 try = 3088
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 82.8863                  try = 3089
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 97.40400000000001        try = 3090
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 97.2882                  try = 3091
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 108.2227                 try = 3092
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 97.6202                  try = 3093
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 108.1429                 try = 3094
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 110.92669999999998       try = 3095
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 117.86619999999999       try = 3096
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 95.538                   try = 3097
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 108.04570000000001       try = 3098
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 108.26650000000001       try = 3099
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 117.191                  try = 3100
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 108.1743                 try = 3101
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 116.687                  try = 3102
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 119.8074                 try = 3103
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1]  cost = 124.73689999999999       try = 3104
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 83.71860000000001        try = 3105
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 100.24210000000001       try = 3106
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 96.6823                  try = 3107
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 109.62260000000003       try = 3108
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 96.30309999999999        try = 3109
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 108.83160000000002       try = 3110
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 108.17140000000002       try = 3111
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 117.11670000000001       try = 3112
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 96.9685                  try = 3113
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 111.48200000000003       try = 3114
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 108.25880000000002       try = 3115
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 119.18910000000001       try = 3116
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 107.45540000000001       try = 3117
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 117.9739                 try = 3118
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 117.6503                 try = 3119
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1]  cost = 124.5856                 try = 3120
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 96.1536                  try = 3121
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 109.27130000000001       try = 3122
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 108.29270000000001       try = 3123
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 117.8272                 try = 3124
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 108.01689999999999       try = 3125
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 117.13959999999999       try = 3126
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 119.06059999999998       try = 3127
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 124.60009999999998       try = 3128
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 107.8673                 try = 3129
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 118.97500000000001       try = 3130
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 118.333                  try = 3131
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 125.85750000000002       try = 3132
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 117.633                  try = 3133
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 124.74569999999999       try = 3134
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 127.0033                 try = 3135
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1]  cost = 130.5328                 try = 3136
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 98.24659999999999        try = 3137
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 107.11470000000001       try = 3138
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 104.20169999999999       try = 3139
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 109.48660000000002       try = 3140
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 104.8631                 try = 3141
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 109.73620000000003       try = 3142
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 109.72280000000002       try = 3143
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 111.01270000000002       try = 3144
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 103.7973                 try = 3145
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 110.65540000000003       try = 3146
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 108.07900000000002       try = 3147
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 111.35390000000002       try = 3148
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 108.31620000000002       try = 3149
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 111.17930000000003       try = 3150
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 111.50250000000001       try = 3151
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1]  cost = 110.78240000000001       try = 3152
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 103.88019999999999       try = 3153
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 109.34250000000002       try = 3154
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 109.01070000000001       try = 3155
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 110.88980000000002       try = 3156
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 109.7755                 try = 3157
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 111.2428                 try = 3158
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 113.81060000000001       try = 3159
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 111.6947                 try = 3160
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 107.8947                 try = 3161
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 111.34700000000002       try = 3162
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 111.35180000000003       try = 3163
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 111.22090000000003       try = 3164
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 111.6924                 try = 3165
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 111.14970000000001       try = 3166
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 114.0541                 try = 3167
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1]  cost = 109.92820000000002       try = 3168
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 104.65310000000001       try = 3169
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 112.12120000000003       try = 3170
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 108.34540000000001       try = 3171
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 112.23030000000004       try = 3172
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 108.399                  try = 3173
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 111.87210000000003       try = 3174
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 110.99590000000003       try = 3175
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 110.88580000000003       try = 3176
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 109.26580000000001       try = 3177
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 114.72390000000004       try = 3178
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 111.28470000000003       try = 3179
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 113.15960000000003       try = 3180
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 110.91410000000002       try = 3181
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 112.37720000000003       try = 3182
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 111.83760000000002       try = 3183
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1]  cost = 109.71750000000003       try = 3184
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 108.0151                 try = 3185
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 112.07740000000001       try = 3186
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 110.88280000000002       try = 3187
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 111.36190000000003       try = 3188
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 111.03980000000001       try = 3189
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 111.10710000000002       try = 3190
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 112.81210000000002       try = 3191
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 109.29620000000003       try = 3192
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 111.0916                 try = 3193
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 113.14390000000003       try = 3194
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 112.28590000000001       try = 3195
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 110.75500000000004       try = 3196
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 112.01870000000001       try = 3197
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 110.07600000000002       try = 3198
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 112.11760000000001       try = 3199
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1]  cost = 106.59170000000003       try = 3200
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 108.3944                 try = 3201
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 113.08310000000003       try = 3202
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 111.30830000000002       try = 3203
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 112.41380000000002       try = 3204
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 112.07830000000001       try = 3205
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 112.77200000000002       try = 3206
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 113.89680000000001       try = 3207
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 111.00730000000003       try = 3208
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 110.35450000000002       try = 3209
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 113.03320000000002       try = 3210
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 111.59500000000001       try = 3211
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 110.69050000000004       try = 3212
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 111.94080000000001       try = 3213
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 110.62450000000003       try = 3214
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 112.08590000000002       try = 3215
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1]  cost = 107.18640000000002       try = 3216
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 110.92060000000001       try = 3217
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 112.2035                 try = 3218
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 113.0099                 try = 3219
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 110.70960000000002       try = 3220
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 113.8833                 try = 3221
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 111.17120000000001       try = 3222
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 114.8772                 try = 3223
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 108.58189999999999       try = 3224
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 111.3445                 try = 3225
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 110.61740000000002       try = 3226
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 111.7604                 try = 3227
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 107.45010000000002       try = 3228
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 112.2096                 try = 3229
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 107.48750000000001       try = 3230
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 111.53010000000002       try = 3231
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1]  cost = 103.22480000000002       try = 3232
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 110.98730000000002       try = 3233
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 114.27600000000002       try = 3234
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 111.63840000000002       try = 3235
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 111.34390000000003       try = 3236
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 111.80060000000002       try = 3237
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 111.09430000000003       try = 3238
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 111.35630000000002       try = 3239
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 107.06680000000001       try = 3240
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 112.00940000000001       try = 3241
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 113.28810000000003       try = 3242
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 110.98710000000001       try = 3243
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 108.68260000000002       try = 3244
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 110.72510000000001       try = 3245
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 108.00880000000002       try = 3246
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 108.60740000000001       try = 3247
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1]  cost = 102.30790000000002       try = 3248
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 111.2419                 try = 3249
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 111.12480000000002       try = 3250
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 111.06840000000001       try = 3251
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 107.36810000000001       try = 3252
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 111.334                  try = 3253
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 107.2219                 try = 3254
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 110.0651                 try = 3255
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 102.36980000000001       try = 3256
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 110.7278                 try = 3257
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 108.60070000000002       try = 3258
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 108.88090000000001       try = 3259
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 103.17060000000002       try = 3260
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 108.7223                 try = 3261
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 102.60020000000002       try = 3262
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 105.78000000000002       try = 3263
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1]  cost = 96.07470000000002        try = 3264
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 133.09110000000004       try = 3265
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 128.72440000000003       try = 3266
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 126.73360000000002       try = 3267
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 118.78370000000002       try = 3268
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 127.9364                 try = 3269
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 119.57470000000002       try = 3270
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 120.48350000000002       try = 3271
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 108.53860000000003       try = 3272
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 126.41400000000002       try = 3273
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 120.03730000000002       try = 3274
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 118.38310000000001       try = 3275
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 108.42320000000002       try = 3276
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 119.16170000000001       try = 3277
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 108.79000000000002       try = 3278
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 110.03540000000001       try = 3279
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]  cost = 96.08050000000003        try = 3280
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 126.5443                 try = 3281
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 118.77180000000001       try = 3282
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 119.3622                 try = 3283
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 108.00650000000002       try = 3284
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 120.6684                 try = 3285
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 108.90090000000001       try = 3286
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 112.3909                 try = 3287
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 97.04020000000001        try = 3288
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 118.331                  try = 3289
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 108.54850000000002       try = 3290
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 109.47550000000001       try = 3291
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 96.1098                  try = 3292
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 110.3575                 try = 3293
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 96.58000000000001        try = 3294
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 100.4066                 try = 3295
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1]  cost = 83.04590000000002        try = 3296
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 126.55160000000001       try = 3297
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 120.78490000000002       try = 3298
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 117.93130000000001       try = 3299
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 108.58140000000003       try = 3300
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 118.5263                 try = 3301
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 108.76460000000002       try = 3302
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 108.81060000000001       try = 3303
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 95.46570000000004        try = 3304
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 118.9365                 try = 3305
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 111.15980000000002       try = 3306
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 108.64280000000001       try = 3307
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 97.28290000000003        try = 3308
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 108.8136                 try = 3309
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 97.04190000000001        try = 3310
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 97.42450000000001        try = 3311
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1]  cost = 82.06960000000002        try = 3312
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 117.7332                 try = 3313
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 108.56070000000001       try = 3314
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 108.2883                 try = 3315
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 95.53260000000002        try = 3316
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 108.9867                 try = 3317
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 95.8192                  try = 3318
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 98.44640000000001        try = 3319
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 81.6957                  try = 3320
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 108.5819                 try = 3321
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 97.3994                  try = 3322
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 97.4636                  try = 3323
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 82.6979                  try = 3324
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 97.7378                  try = 3325
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 82.5603                  try = 3326
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 85.5241                  try = 3327
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1]  cost = 66.7634                  try = 3328
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 102.75189999999999       try = 3329
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 109.42380000000001       try = 3330
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 107.35760000000002       try = 3331
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 110.44630000000002       try = 3332
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 108.02860000000001       try = 3333
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 110.70550000000001       try = 3334
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 111.53890000000001       try = 3335
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 110.63260000000001       try = 3336
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 106.56680000000001       try = 3337
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 111.22870000000002       try = 3338
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 109.49910000000001       try = 3339
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 110.57780000000001       try = 3340
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 109.7459                 try = 3341
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 110.4128                 try = 3342
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 111.5828                 try = 3343
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1]  cost = 108.6665                 try = 3344
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 106.9495                 try = 3345
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 110.21560000000002       try = 3346
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 110.73060000000001       try = 3347
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 110.4135                 try = 3348
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 111.505                  try = 3349
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 110.77610000000001       try = 3350
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 114.19069999999999       try = 3351
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 109.8786                 try = 3352
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 109.2282                 try = 3353
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 110.48430000000002       try = 3354
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 111.33590000000001       try = 3355
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 109.00880000000002       try = 3356
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 111.6861                 try = 3357
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 108.94720000000002       try = 3358
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 112.6984                 try = 3359
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1]  cost = 106.3763                 try = 3360
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 107.2564                 try = 3361
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 112.52830000000002       try = 3362
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 109.59930000000001       try = 3363
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 111.28800000000003       try = 3364
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 109.66250000000001       try = 3365
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 110.9394                 try = 3366
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 110.91000000000001       try = 3367
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 108.60370000000002       try = 3368
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 110.1333                 try = 3369
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 113.39520000000002       try = 3370
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 110.8028                 try = 3371
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 110.48150000000003       try = 3372
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 110.4418                 try = 3373
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 109.70870000000002       try = 3374
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 110.0159                 try = 3375
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1]  cost = 105.69960000000002       try = 3376
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 109.1824                 try = 3377
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 111.0485                 try = 3378
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 110.7007                 try = 3379
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 108.98360000000001       try = 3380
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 110.86729999999999       try = 3381
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 108.7384                 try = 3382
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 111.2902                 try = 3383
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 105.57809999999999       try = 3384
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 110.5231                 try = 3385
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 110.37920000000001       try = 3386
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 110.36800000000001       try = 3387
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 106.64090000000002       try = 3388
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 110.1104                 try = 3389
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 105.9715                 try = 3390
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 108.85990000000001       try = 3391
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1]  cost = 101.1378                 try = 3392
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 129.1912                 try = 3393
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 126.80770000000003       try = 3394
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 124.52550000000001       try = 3395
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 118.55880000000002       try = 3396
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 125.6293                 try = 3397
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 119.25080000000003       try = 3398
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 119.86820000000002       try = 3399
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 109.90650000000004       try = 3400
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 124.3689                 try = 3401
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 119.97540000000001       try = 3402
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 118.02980000000001       try = 3403
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 110.05310000000001       try = 3404
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 118.7094                 try = 3405
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 110.32090000000002       try = 3406
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 111.27490000000002       try = 3407
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1]  cost = 99.30320000000002        try = 3408
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 124.3158                 try = 3409
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 118.5265                 try = 3410
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 118.82549999999999       try = 3411
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 109.453                  try = 3412
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 120.03269999999999       try = 3413
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 110.2484                 try = 3414
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 113.447                  try = 3415
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 100.07950000000001       try = 3416
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 117.9573                 try = 3417
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 110.15800000000002       try = 3418
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 110.79360000000001       try = 3419
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 99.41110000000002        try = 3420
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 111.57659999999998       try = 3421
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 99.7823                  try = 3422
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 103.31750000000001       try = 3423
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1]  cost = 87.94                    try = 3424
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 124.5633                 try = 3425
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 120.77980000000002       try = 3426
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 117.63480000000003       try = 3427
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 110.26810000000002       try = 3428
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 118.1308                 try = 3429
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 110.35230000000001       try = 3430
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 110.10690000000001       try = 3431
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 98.74520000000003        try = 3432
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 118.803                  try = 3433
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 113.00950000000003       try = 3434
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 110.20110000000001       try = 3435
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 100.82440000000001       try = 3436
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 110.27289999999999       try = 3437
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 100.48440000000002       try = 3438
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 100.5756                 try = 3439
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1]  cost = 87.20390000000002        try = 3440
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 117.41629999999999       try = 3441
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 110.227                  try = 3442
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 109.6632                 try = 3443
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 98.89070000000001        try = 3444
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 110.26259999999998       try = 3445
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 99.07829999999998        try = 3446
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 101.41409999999999       try = 3447
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 86.64659999999999        try = 3448
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 110.1198                 try = 3449
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 100.9205                 try = 3450
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 100.69330000000001       try = 3451
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 87.91080000000002        try = 3452
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 100.8685                 try = 3453
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 87.6742                  try = 3454
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 90.34660000000001        try = 3455
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1]  cost = 73.5691                  try = 3456
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 140.72160000000002       try = 3457
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 134.1587                 try = 3458
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 133.01470000000003       try = 3459
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 122.86860000000003       try = 3460
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 134.2271                 try = 3461
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 123.66920000000002       try = 3462
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 125.42480000000002       try = 3463
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 111.28370000000002       try = 3464
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 132.30870000000002       try = 3465
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 123.73580000000004       try = 3466
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 122.92840000000002       try = 3467
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 110.77230000000002       try = 3468
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 123.7166                 try = 3469
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 111.14870000000002       try = 3470
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 113.2409                 try = 3471
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1]  cost = 97.08980000000001        try = 3472
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 132.7388                 try = 3473
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 122.7701                 try = 3474
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 124.20729999999999       try = 3475
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 110.6554                 try = 3476
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 125.52309999999999       try = 3477
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 111.5594                 try = 3478
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 115.8962                 try = 3479
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 98.3493                  try = 3480
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 122.7897                 try = 3481
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 110.811                  try = 3482
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 112.58480000000002       try = 3483
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 97.0229                  try = 3484
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 113.4764                 try = 3485
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 97.50269999999999        try = 3486
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 102.1761                 try = 3487
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1]  cost = 82.6192                  try = 3488
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 132.2801                 try = 3489
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 124.31720000000001       try = 3490
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 122.3104                 try = 3491
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 110.76430000000003       try = 3492
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 122.91499999999999       try = 3493
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 110.95710000000003       try = 3494
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 111.8499                 try = 3495
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 96.3088                  try = 3496
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 122.92920000000001       try = 3497
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 112.95630000000003       try = 3498
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 111.28610000000002       try = 3499
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 97.73000000000003        try = 3500
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 111.4665                 try = 3501
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 97.49860000000001        try = 3502
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 98.728                   try = 3503
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1]  cost = 81.17690000000002        try = 3504
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 122.02569999999999       try = 3505
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 110.657                  try = 3506
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 111.23140000000001       try = 3507
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 96.27950000000001        try = 3508
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 111.93939999999999       try = 3509
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 96.5757                  try = 3510
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 100.0497                 try = 3511
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 81.1028                  try = 3512
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 111.13859999999998       try = 3513
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 97.7599                  try = 3514
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 98.6709                  try = 3515
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 81.709                   try = 3516
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 98.95469999999999        try = 3517
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 81.58099999999999        try = 3518
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 85.3916                  try = 3519
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1]  cost = 64.4347                  try = 3520
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 161.79070000000004       try = 3521
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 146.1724                 try = 3522
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 144.8124                 try = 3523
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 125.61090000000003       try = 3524
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 146.4576                 try = 3525
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 126.8443                 try = 3526
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 128.3839                 try = 3527
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 105.18740000000001       try = 3528
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 144.7406                 try = 3529
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 127.11230000000003       try = 3530
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 126.08890000000001       try = 3531
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 104.87740000000004       try = 3532
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 127.3099                 try = 3533
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 105.68660000000003       try = 3534
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 107.56280000000001       try = 3535
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1]  cost = 82.35630000000002        try = 3536
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 144.7349                 try = 3537
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 125.7108                 try = 3538
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 126.932                  try = 3539
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 104.3247                 try = 3540
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 128.6806                 try = 3541
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 105.6615                 try = 3542
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 109.78229999999999       try = 3543
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 83.18                    try = 3544
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 126.1486                 try = 3545
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 105.1145                 try = 3546
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 106.67229999999999       try = 3547
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 82.05499999999999        try = 3548
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 107.99669999999999       try = 3549
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 82.9676                  try = 3550
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 87.42499999999998        try = 3551
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1]  cost = 58.81270000000001        try = 3552
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 144.2168                 try = 3553
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 127.19850000000002       try = 3554
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 124.9757                 try = 3555
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 104.37420000000002       try = 3556
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 126.01310000000001       try = 3557
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 104.99980000000002       try = 3558
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 105.6766                 try = 3559
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 81.08010000000002        try = 3560
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 126.2287                 try = 3561
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 107.20040000000003       try = 3562
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 105.31420000000001       try = 3563
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 82.70270000000002        try = 3564
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 105.92739999999998       try = 3565
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 82.90410000000001        try = 3566
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 83.9175                  try = 3567
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1]  cost = 57.311                   try = 3568
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 124.8894                 try = 3569
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 104.46530000000001       try = 3570
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 104.8237                 try = 3571
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 80.81640000000002        try = 3572
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 105.96449999999999       try = 3573
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 81.5454                  try = 3574
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 84.8034                  try = 3575
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 56.8011                  try = 3576
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 105.3651                 try = 3577
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 82.93100000000001        try = 3578
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 83.62599999999999        try = 3579
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 57.6087                  try = 3580
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 84.34259999999998        try = 3581
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 57.9135                  try = 3582
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 61.5081                  try = 3583
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1]  cost = 31.495799999999996       try = 3584
case = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 95.44189999999999        try = 3585
case = [1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 105.03000000000002       try = 3586
case = [0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 102.3932                 try = 3587
case = [1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 108.39810000000001       try = 3588
case = [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 102.98239999999998       try = 3589
case = [1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 108.5755                 try = 3590
case = [0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 108.8383                 try = 3591
case = [1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 110.84820000000003       try = 3592
case = [0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 101.8994                 try = 3593
case = [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 109.47750000000002       try = 3594
case = [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 107.17730000000002       try = 3595
case = [1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 111.17220000000003       try = 3596
case = [0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 107.34230000000001       try = 3597
case = [1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 110.92540000000002       try = 3598
case = [0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 111.52480000000003       try = 3599
case = [1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1]  cost = 111.52470000000001       try = 3600
case = [0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 102.0073                 try = 3601
case = [1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 108.18960000000001       try = 3602
case = [0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 108.13400000000001       try = 3603
case = [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 110.73310000000004       try = 3604
case = [0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 108.8266                 try = 3605
case = [1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 111.0139                 try = 3606
case = [0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 113.85790000000001       try = 3607
case = [1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 112.46200000000002       try = 3608
case = [0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 106.92859999999999       try = 3609
case = [1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 111.10090000000002       try = 3610
case = [0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 111.38190000000002       try = 3611
case = [1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 111.97100000000005       try = 3612
case = [0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 111.65030000000002       try = 3613
case = [1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 111.82760000000003       try = 3614
case = [0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 115.0082                 try = 3615
case = [1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1]  cost = 111.60230000000003       try = 3616
case = [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 102.7056                 try = 3617
case = [1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 110.89370000000002       try = 3618
case = [0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 107.39410000000002       try = 3619
case = [1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 111.99900000000004       try = 3620
case = [0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 107.3755                 try = 3621
case = [1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 111.56860000000002       try = 3622
case = [0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 110.96860000000002       try = 3623
case = [1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 111.57850000000003       try = 3624
case = [0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 108.22510000000001       try = 3625
case = [1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 114.40320000000004       try = 3626
case = [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 111.24020000000003       try = 3627
case = [1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 113.83510000000003       try = 3628
case = [0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 110.79740000000002       try = 3629
case = [1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 112.98050000000002       try = 3630
case = [0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 112.71710000000002       try = 3631
case = [1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1]  cost = 111.31700000000001       try = 3632
case = [0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 106.99940000000001       try = 3633
case = [1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 111.78170000000001       try = 3634
case = [0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 110.86330000000002       try = 3635
case = [1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 112.06240000000003       try = 3636
case = [0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 110.94810000000001       try = 3637
case = [1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 111.73540000000003       try = 3638
case = [0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 113.7166                 try = 3639
case = [1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 110.92070000000001       try = 3640
case = [0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 110.98270000000002       try = 3641
case = [1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 113.75500000000004       try = 3642
case = [0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 113.17320000000002       try = 3643
case = [1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 112.36230000000002       try = 3644
case = [0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 112.83380000000001       try = 3645
case = [1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 111.61110000000001       try = 3646
case = [0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 113.92889999999998       try = 3647
case = [1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1]  cost = 109.12299999999999       try = 3648
case = [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 123.94680000000001       try = 3649
case = [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 124.47950000000003       try = 3650
case = [0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 121.62670000000001       try = 3651
case = [1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 118.57620000000004       try = 3652
case = [0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 122.6487                 try = 3653
case = [1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 119.18640000000003       try = 3654
case = [0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 119.23320000000002       try = 3655
case = [1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 112.18770000000002       try = 3656
case = [0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 121.7671                 try = 3657
case = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 120.28980000000003       try = 3658
case = [0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 117.77360000000003       try = 3659
case = [1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 112.71310000000003       try = 3660
case = [0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 118.37140000000002       try = 3661
case = [1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 112.89910000000003       try = 3662
case = [0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 113.28250000000001       try = 3663
case = [1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1]  cost = 104.22700000000003       try = 3664
case = [0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 121.43919999999999       try = 3665
case = [1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 118.5661                 try = 3666
case = [0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 118.29450000000001       try = 3667
case = [1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 111.83820000000004       try = 3668
case = [0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 119.4199                 try = 3669
case = [1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 112.55180000000003       try = 3670
case = [0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 115.17980000000001       try = 3671
case = [1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 104.72850000000003       try = 3672
case = [0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 117.72330000000001       try = 3673
case = [1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 112.84020000000002       try = 3674
case = [0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 112.90520000000002       try = 3675
case = [1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 104.43890000000003       try = 3676
case = [0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 113.60640000000001       try = 3677
case = [1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 104.72830000000003       try = 3678
case = [0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 107.69290000000001       try = 3679
case = [1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1]  cost = 95.23160000000003        try = 3680
case = [0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 122.0781                 try = 3681
case = [1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 121.21080000000003       try = 3682
case = [0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 117.49520000000003       try = 3683
case = [1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 113.04470000000002       try = 3684
case = [0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 117.9094                 try = 3685
case = [1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 113.04710000000001       try = 3686
case = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 112.23110000000003       try = 3687
case = [1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 103.78560000000003       try = 3688
case = [0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 118.9604                 try = 3689
case = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 116.08310000000002       try = 3690
case = [0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 112.70410000000003       try = 3691
case = [1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 106.24360000000003       try = 3692
case = [0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 112.69410000000002       try = 3693
case = [1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 105.82180000000002       try = 3694
case = [0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 105.34240000000003       try = 3695
case = [1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1]  cost = 94.88690000000003        try = 3696
case = [0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 117.2989                 try = 3697
case = [1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 113.02580000000002       try = 3698
case = [0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 111.89140000000002       try = 3699
case = [1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 104.03510000000003       try = 3700
case = [0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 112.409                  try = 3701
case = [1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 104.14090000000002       try = 3702
case = [0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 105.90610000000001       try = 3703
case = [1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 94.05480000000001        try = 3704
case = [0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 112.64500000000001       try = 3705
case = [1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 106.36190000000002       try = 3706
case = [0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 105.56410000000001       try = 3707
case = [1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 95.69780000000003        try = 3708
case = [0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 105.6575                 try = 3709
case = [1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 95.37940000000002        try = 3710
case = [0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 97.48119999999999        try = 3711
case = [1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1]  cost = 83.61990000000002        try = 3712
case = [0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 130.35760000000002       try = 3713
case = [1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 126.71090000000002       try = 3714
case = [0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 124.99630000000003       try = 3715
case = [1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 117.76640000000003       try = 3716
case = [0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 126.12690000000002       try = 3717
case = [1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 118.48520000000002       try = 3718
case = [0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 119.67020000000002       try = 3719
case = [1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 108.44530000000003       try = 3720
case = [0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 124.58730000000001       try = 3721
case = [1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 118.93060000000003       try = 3722
case = [0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 117.55260000000003       try = 3723
case = [1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 108.31270000000004       try = 3724
case = [0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 118.25900000000001       try = 3725
case = [1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 108.60730000000002       try = 3726
case = [0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 110.12890000000002       try = 3727
case = [1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1]  cost = 96.89400000000003        try = 3728
case = [0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 124.74260000000001       try = 3729
case = [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 117.69010000000003       try = 3730
case = [0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 118.55670000000002       try = 3731
case = [1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 107.92100000000002       try = 3732
case = [0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 119.79070000000002       try = 3733
case = [1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 108.74320000000002       try = 3734
case = [0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 112.5094                 try = 3735
case = [1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 97.87870000000002        try = 3736
case = [0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 117.43610000000001       try = 3737
case = [1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 108.37360000000002       try = 3738
case = [0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 109.57680000000002       try = 3739
case = [1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 96.93110000000001        try = 3740
case = [0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 110.3866                 try = 3741
case = [1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 97.32910000000003        try = 3742
case = [0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 101.43190000000001       try = 3743
case = [1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1]  cost = 84.79120000000002        try = 3744
case = [0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 124.67530000000001       try = 3745
case = [1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 119.62860000000002       try = 3746
case = [0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 117.05120000000002       try = 3747
case = [1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 108.42130000000004       try = 3748
case = [0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 117.57400000000001       try = 3749
case = [1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 108.53230000000002       try = 3750
case = [0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 108.85450000000002       try = 3751
case = [1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 96.22960000000003        try = 3752
case = [0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 117.96700000000001       try = 3753
case = [1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 110.91030000000003       try = 3754
case = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 108.66950000000001       try = 3755
case = [1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 98.02960000000004        try = 3756
case = [0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 108.7681                 try = 3757
case = [1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 97.71640000000002        try = 3758
case = [0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 98.3752                  try = 3759
case = [1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1]  cost = 83.74030000000003        try = 3760
case = [0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 116.7887                 try = 3761
case = [1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 108.33620000000002       try = 3762
case = [0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 108.34000000000002       try = 3763
case = [1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 96.30430000000001        try = 3764
case = [0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 108.96620000000001       try = 3765
case = [1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 96.51870000000001        try = 3766
case = [0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 99.42210000000001        try = 3767
case = [1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 83.3914                  try = 3768
case = [0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 108.54420000000002       try = 3769
case = [1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 98.08170000000001        try = 3770
case = [0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 98.4221                  try = 3771
case = [1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 84.3764                  try = 3772
case = [0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 98.6241                  try = 3773
case = [1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 84.1666                  try = 3774
case = [0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 87.40660000000001        try = 3775
case = [1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1]  cost = 69.3659                  try = 3776
case = [0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 153.49230000000003       try = 3777
case = [1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 140.79020000000003       try = 3778
case = [0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 138.8596                 try = 3779
case = [1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 122.57430000000004       try = 3780
case = [0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 140.423                  try = 3781
case = [1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 123.72590000000004       try = 3782
case = [0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 124.69490000000002       try = 3783
case = [1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 104.41460000000004       try = 3784
case = [0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 139.0848                 try = 3785
case = [1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 124.37270000000005       try = 3786
case = [0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 122.77870000000003       try = 3787
case = [1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 104.48340000000003       try = 3788
case = [0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 123.9179                 try = 3789
case = [1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 105.21080000000002       try = 3790
case = [0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 106.51640000000002       try = 3791
case = [1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1]  cost = 84.2261                  try = 3792
case = [0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 138.80429999999998       try = 3793
case = [1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 122.69640000000004       try = 3794
case = [0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 123.34700000000001       try = 3795
case = [1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 103.65590000000003       try = 3796
case = [0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 125.0138                 try = 3797
case = [1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 104.91090000000001       try = 3798
case = [0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 108.4611                 try = 3799
case = [1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 84.775                   try = 3800
case = [0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 122.8606                 try = 3801
case = [1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 104.74270000000003       try = 3802
case = [0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 105.7299                 try = 3803
case = [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 84.0288                  try = 3804
case = [0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 106.9725                 try = 3805
case = [1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 84.8596                  try = 3806
case = [0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 88.7464                  try = 3807
case = [1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1]  cost = 63.0503                  try = 3808
case = [0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 138.67759999999998       try = 3809
case = [1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 124.57550000000002       try = 3810
case = [0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 121.78210000000003       try = 3811
case = [1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 104.09680000000002       try = 3812
case = [0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 122.73770000000002       try = 3813
case = [1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 104.64060000000002       try = 3814
case = [0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 104.74680000000002       try = 3815
case = [1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 83.06650000000002        try = 3816
case = [0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 123.33210000000001       try = 3817
case = [1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 107.22000000000001       try = 3818
case = [0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 104.76320000000003       try = 3819
case = [1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 85.06790000000002        try = 3820
case = [0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 105.29460000000002       try = 3821
case = [1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 85.18750000000001        try = 3822
case = [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 85.6303                  try = 3823
case = [1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1]  cost = 61.93999999999999        try = 3824
case = [0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 121.718                  try = 3825
case = [1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 104.21010000000003       try = 3826
case = [0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 103.9979                 try = 3827
case = [1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 82.90680000000002        try = 3828
case = [0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 105.0569                 try = 3829
case = [1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 83.55400000000002        try = 3830
case = [0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 86.2414                  try = 3831
case = [1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 61.155300000000004       try = 3832
case = [0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 104.8363                 try = 3833
case = [1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 85.3184                  try = 3834
case = [0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 85.44279999999999        try = 3835
case = [1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 62.34170000000001        try = 3836
case = [0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 86.07759999999999        try = 3837
case = [1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 62.564699999999995       try = 3838
case = [0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 65.58869999999999        try = 3839
case = [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1]  cost = 38.492599999999996       try = 3840
case = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 126.7891                 try = 3841
case = [1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 125.12560000000005       try = 3842
case = [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 123.11960000000003       try = 3843
case = [1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 117.87290000000004       try = 3844
case = [0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 124.15120000000002       try = 3845
case = [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 118.49270000000004       try = 3846
case = [0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 119.38630000000003       try = 3847
case = [1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 110.14460000000004       try = 3848
case = [0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 122.87360000000002       try = 3849
case = [1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 119.20010000000003       try = 3850
case = [0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 117.53070000000004       try = 3851
case = [1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 110.27400000000004       try = 3852
case = [0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 118.13810000000004       try = 3853
case = [1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 110.46960000000004       try = 3854
case = [0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 111.69980000000002       try = 3855
case = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]  cost = 100.44810000000004       try = 3856
case = [0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 122.84550000000002       try = 3857
case = [1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 117.77620000000003       try = 3858
case = [0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 118.35140000000004       try = 3859
case = [1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 109.69890000000004       try = 3860
case = [0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 119.4864                 try = 3861
case = [1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 110.42210000000003       try = 3862
case = [0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 113.89690000000002       try = 3863
case = [1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 101.24940000000002       try = 3864
case = [0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 117.39380000000001       try = 3865
case = [1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 110.31450000000002       try = 3866
case = [0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 111.22630000000002       try = 3867
case = [1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 100.56380000000004       try = 3868
case = [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 111.93710000000002       try = 3869
case = [1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 100.86280000000004       try = 3870
case = [0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 104.67420000000001       try = 3871
case = [1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1]  cost = 90.01670000000003        try = 3872
case = [0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 123.01840000000001       try = 3873
case = [1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 119.95490000000004       try = 3874
case = [0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 117.08610000000003       try = 3875
case = [1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 110.43940000000003       try = 3876
case = [0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 117.5099                 try = 3877
case = [1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 110.45140000000004       try = 3878
case = [0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 110.48220000000002       try = 3879
case = [1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 99.84050000000003        try = 3880
case = [0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 118.16490000000002       try = 3881
case = [1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 113.09140000000004       try = 3882
case = [0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 110.55920000000002       try = 3883
case = [1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 101.90250000000003       try = 3884
case = [0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 110.55880000000002       try = 3885
case = [1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 101.49030000000003       try = 3886
case = [0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 101.85770000000001       try = 3887
case = [1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1]  cost = 89.20600000000003        try = 3888
case = [0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 116.8032                 try = 3889
case = [1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 110.33390000000003       try = 3890
case = [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 110.04630000000002       try = 3891
case = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 99.99380000000004        try = 3892
case = [0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 110.57350000000001       try = 3893
case = [1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 100.10920000000003       try = 3894
case = [0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 102.72120000000001       try = 3895
case = [1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 88.67370000000003        try = 3896
case = [0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 110.41350000000001       try = 3897
case = [1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 101.93420000000002       try = 3898
case = [0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 101.98320000000001       try = 3899
case = [1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 89.92070000000002        try = 3900
case = [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 102.0862                 try = 3901
case = [1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 89.61190000000002        try = 3902
case = [0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 92.5605                  try = 3903
case = [1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1]  cost = 76.50300000000003        try = 3904
case = [0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 151.6664                 try = 3905
case = [1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 140.94750000000002       try = 3906
case = [0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 138.7255                 try = 3907
case = [1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 124.42340000000004       try = 3908
case = [0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 140.1899                 try = 3909
case = [1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 125.47600000000004       try = 3910
case = [0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 126.15360000000003       try = 3911
case = [1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 107.85650000000004       try = 3912
case = [0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 139.1137                 try = 3913
case = [1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 126.38480000000004       try = 3914
case = [0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 124.49940000000002       try = 3915
case = [1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 108.18730000000005       try = 3916
case = [0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 125.53960000000002       try = 3917
case = [1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 108.81570000000004       try = 3918
case = [0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 109.82990000000002       try = 3919
case = [1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1]  cost = 89.52280000000002        try = 3920
case = [0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 138.6498                 try = 3921
case = [1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 124.52510000000004       try = 3922
case = [0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 124.88430000000002       try = 3923
case = [1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 107.17640000000003       try = 3924
case = [0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 126.45210000000002       try = 3925
case = [1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 108.33240000000002       try = 3926
case = [0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 111.59120000000001       try = 3927
case = [1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 89.88830000000002        try = 3928
case = [0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 124.56090000000002       try = 3929
case = [1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 108.42620000000002       try = 3930
case = [0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 109.12200000000001       try = 3931
case = [1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 89.40410000000001        try = 3932
case = [0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 110.2656                 try = 3933
case = [1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 90.13590000000002        try = 3934
case = [0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 93.73130000000002        try = 3935
case = [1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1]  cost = 70.01840000000001        try = 3936
case = [0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 138.7633                 try = 3937
case = [1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 126.64440000000003       try = 3938
case = [0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 123.55960000000002       try = 3939
case = [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 107.85750000000004       try = 3940
case = [0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 124.41620000000002       try = 3941
case = [1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 108.30230000000003       try = 3942
case = [0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 108.11710000000002       try = 3943
case = [1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 88.42000000000003        try = 3944
case = [0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 125.27260000000003       try = 3945
case = [1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 111.14370000000002       try = 3946
case = [0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 108.39550000000003       try = 3947
case = [1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 90.68340000000002        try = 3948
case = [0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 108.8279                 try = 3949
case = [1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 90.70400000000002        try = 3950
case = [0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 90.8554                  try = 3951
case = [1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1]  cost = 69.1483                  try = 3952
case = [0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 123.47510000000001       try = 3953
case = [1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 107.95040000000002       try = 3954
case = [0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 107.44680000000002       try = 3955
case = [1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 88.33890000000002        try = 3956
case = [0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 108.4068                 try = 3957
case = [1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 88.8871                  try = 3958
case = [0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 91.2831                  try = 3959
case = [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 68.18020000000001        try = 3960
case = [0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 108.44820000000001       try = 3961
case = [1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 90.91350000000001        try = 3962
case = [0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 90.74650000000001        try = 3963
case = [1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 69.62860000000002        try = 3964
case = [0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 91.2823                  try = 3965
case = [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 69.7526                  try = 3966
case = [0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 72.48519999999999        try = 3967
case = [1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1]  cost = 47.3723                  try = 3968
case = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 159.45980000000003       try = 3969
case = [1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 144.56150000000002       try = 3970
case = [0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 143.4777                 try = 3971
case = [1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 124.99620000000004       try = 3972
case = [0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 145.0507                 try = 3973
case = [1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 126.15740000000004       try = 3974
case = [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 127.97320000000002       try = 3975
case = [1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 105.49670000000003       try = 3976
case = [0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 143.3165                 try = 3977
case = [1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 126.40820000000004       try = 3978
case = [0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 125.66100000000002       try = 3979
case = [1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 105.16950000000003       try = 3980
case = [0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 126.80980000000001       try = 3981
case = [1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 105.90650000000002       try = 3982
case = [0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 108.05890000000002       try = 3983
case = [1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1]  cost = 83.5724                  try = 3984
case = [0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 143.3358                 try = 3985
case = [1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 125.03170000000003       try = 3986
case = [0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 126.52910000000001       try = 3987
case = [1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 104.64180000000003       try = 3988
case = [0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 128.2055                 try = 3989
case = [1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 105.90640000000002       try = 3990
case = [0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 110.30340000000001       try = 3991
case = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 84.4211                  try = 3992
case = [0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 125.65630000000002       try = 3993
case = [1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 105.34220000000003       try = 3994
case = [0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 107.17620000000001       try = 3995
case = [1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 83.27890000000001        try = 3996
case = [0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 108.42840000000001       try = 3997
case = [1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 84.1193                  try = 3998
case = [0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 88.8529                  try = 3999
case = [1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1]  cost = 60.96060000000001        try = 4000
case = [0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 142.7431                 try = 4001
case = [1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 126.44480000000003       try = 4002
case = [0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 124.49820000000001       try = 4003
case = [1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 104.61670000000004       try = 4004
case = [0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 125.46340000000002       try = 4005
case = [1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 105.17010000000003       try = 4006
case = [0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 106.12310000000001       try = 4007
case = [1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 82.24660000000002        try = 4008
case = [0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 125.66180000000001       try = 4009
case = [1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 107.35350000000004       try = 4010
case = [0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 105.74350000000001       try = 4011
case = [1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 83.85200000000002        try = 4012
case = [0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 106.28450000000001       try = 4013
case = [1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 83.98120000000002        try = 4014
case = [0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 85.27080000000001        try = 4015
case = [1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1]  cost = 59.384299999999996       try = 4016
case = [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 124.3475                 try = 4017
case = [1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 104.64340000000003       try = 4018
case = [0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 105.27800000000002       try = 4019
case = [1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 81.9907                  try = 4020
case = [0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 106.34660000000001       try = 4021
case = [1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 82.64750000000001        try = 4022
case = [0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 86.1817                  try = 4023
case = [1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 58.8994                  try = 4024
case = [0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 105.73                   try = 4025
case = [1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 84.0159                  try = 4026
case = [0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 84.9871                  try = 4027
case = [1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 59.6898                  try = 4028
case = [0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 85.63149999999999        try = 4029
case = [1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 59.922399999999996       try = 4030
case = [0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 63.7932                  try = 4031
case = [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1]  cost = 34.500899999999994       try = 4032
case = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 178.96690000000007       try = 4033
case = [1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 155.01320000000004       try = 4034
case = [0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 153.7134                 try = 4035
case = [1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 126.17650000000003       try = 4036
case = [0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 155.71920000000003       try = 4037
case = [1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 127.77050000000003       try = 4038
case = [0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 129.37030000000001       try = 4039
case = [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 97.83840000000004        try = 4040
case = [0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 154.18640000000005       try = 4041
case = [1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 128.22270000000003       try = 4042
case = [0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 127.25950000000002       try = 4043
case = [1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 97.71260000000002        try = 4044
case = [0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 128.8411                 try = 4045
case = [1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 98.88240000000003        try = 4046
case = [0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 100.81880000000001       try = 4047
case = [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1]  cost = 67.2769                  try = 4048
case = [0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 153.76990000000004       try = 4049
case = [1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 126.41040000000004       try = 4050
case = [0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 127.69180000000001       try = 4051
case = [1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 96.74910000000003        try = 4052
case = [0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 129.801                  try = 4053
case = [1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 98.44650000000001        try = 4054
case = [0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 102.62750000000001       try = 4055
case = [1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 67.6898                  try = 4056
case = [0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 127.45320000000001       try = 4057
case = [1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 98.08370000000002        try = 4058
case = [0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 99.70170000000002        try = 4059
case = [1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 66.749                   try = 4060
case = [0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 101.3867                 try = 4061
case = [1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 68.0222                  try = 4062
case = [0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 72.5398                  try = 4063
case = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1]  cost = 35.592099999999995       try = 4064
case = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 153.11780000000002       try = 4065
case = [1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 127.76410000000003       try = 4066
case = [0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 125.6015                 try = 4067
case = [1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 96.66460000000002        try = 4068
case = [0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 126.99950000000003       try = 4069
case = [1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 97.65080000000002        try = 4070
case = [0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 98.38780000000001        try = 4071
case = [1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 65.4559                  try = 4072
case = [0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 127.39930000000001       try = 4073
case = [1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 100.03560000000002       try = 4074
case = [0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 98.20960000000002        try = 4075
case = [1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 67.2627                  try = 4076
case = [0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 99.1834                  try = 4077
case = [1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 67.82469999999999        try = 4078
case = [0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 68.8983                  try = 4079
case = [1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1]  cost = 33.956399999999995       try = 4080
case = [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 125.64920000000001       try = 4081
case = [1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 96.8897                  try = 4082
case = [0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 97.3083                  try = 4083
case = [1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 64.9656                  try = 4084
case = [0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 98.8097                  try = 4085
case = [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 66.0552                  try = 4086
case = [0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 69.3734                  try = 4087
case = [1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 33.035700000000006       try = 4088
case = [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 98.39450000000001        try = 4089
case = [1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 67.625                   try = 4090
case = [0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 68.3802                  try = 4091
case = [1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 34.027499999999996       try = 4092
case = [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 69.45739999999999        try = 4093
case = [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 34.692899999999995       try = 4094
case = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 38.3477                  try = 4095
case = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]  cost = 0.0                      try = 4096

Best case(solution) = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]  cost = 178.96690000000007
In [60]:
draw_graph(G, colors_brute, pos)

Method 2: QAOA¶

In [61]:
from scipy.optimize import minimize
from tqdm import tqdm

expectation = get_expectation(G)
p = 64
res = []
for i in tqdm(range(1, p+1)):
    res.append(minimize(expectation, np.ones(i*2)*np.pi/2,
               method='COBYLA', options={'maxiter': 2500}))

100%|██████████| 64/64 [1:44:38<00:00, 98.10s/it]
In [62]:
approx = []
for i in range(p):
    approx.append(-res[i].fun/best_cost_brute)

x = np.arange(1, p+1, 1)

plt.plot(x, approx, marker='+', c='k', linestyle='--')
plt.ylim((0.5, 1))
plt.xlim(0, p+1)
plt.xlabel('p')
plt.ylabel('Approximation')
plt.grid(True)
plt.show()
In [63]:
best_p = np.argmax(approx)
print("The best p(iterationo number) is", best_p)

The best p(iterationo number) is 41
In [64]:
res[best_p].x
Out[64]:
array([2.60189093, 2.45685172, 1.76406145, 1.69130679, 1.73996513,
       1.78564314, 1.72780398, 1.6455303 , 1.78770161, 1.49961987,
       1.81463721, 1.73730067, 1.67367512, 1.66720455, 2.03830696,
       1.71373839, 1.72883008, 1.8030446 , 1.80194911, 1.7389699 ,
       1.84135531, 1.35609562, 1.66236932, 1.74523151, 1.63831966,
       1.76182302, 1.66578004, 1.75038975, 1.67904789, 1.64253448,
       1.75895467, 2.82033719, 1.44842357, 1.40296791, 1.45963551,
       1.4987131 , 1.49962536, 1.49170507, 1.48020899, 1.51298004,
       1.52377457, 1.43253122, 1.4366814 , 1.41854585, 1.51102883,
       1.50844438, 1.50946707, 1.5140788 , 1.51079755, 1.51200307,
       1.5114401 , 1.5088839 , 1.5109891 , 1.50753512, 1.51000972,
       1.5110181 , 1.58329037, 1.51400208, 1.51169739, 1.51133587,
       1.53308693, 1.52961181, 1.52975485, 1.53763588, 1.53335262,
       1.53141124, 1.54488137, 1.54344385, 1.53057713, 1.52867187,
       1.52824599, 1.53659557, 1.5355529 , 1.52760009, 1.57062045,
       1.55951193, 1.5491585 , 1.56409071, 1.56279086, 1.56774407,
       1.56035   , 1.55876152, 1.55979377, 1.5586412 ])
In [67]:
from qiskit.visualization import plot_histogram
backend = Aer.get_backend('aer_simulator')
backend.shots = 512

qc_res = create_qaoa_circ(G, res[best_p].x)
counts = backend.run(qc_res, seed_simulator=10).result().get_counts()
plot_histogram(counts, figsize=(40, 5), title='512 Shots')
Out[67]:
In [68]:
# # Plot the Quantum Circuit of QAOA
# qc_res.draw(output='mpl', plot_barriers=True).savefig('QAOA_circuit.png', dpi=720)
# qc_res.draw(output='mpl', plot_barriers=True)
In [69]:
# qc_res.draw(output='mpl', plot_barriers=True, fold=-1).savefig('QAOA_circuit(full).png', dpi=720)
# qc_res.draw(output='mpl', plot_barriers=True, fold=-1)
In [70]:
xbest_qaoa = list(map(int, list(max(counts, key=counts.get))))
colors_qaoa = ['g' if xbest_qaoa[i] == 0 else 'c' for i in range(n)]

print('xbest_brute :', xbest_brute)
print('QAOA        :', xbest_qaoa)

xbest_brute : [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0]
QAOA        : [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1]
In [71]:
draw_graph(G, colors_brute, pos)
In [72]:
draw_graph(G, colors_qaoa, pos)
In [73]:
print('Best solution - Brute Force : ' +
      str(xbest_brute) + ',  cost = ' + str(best_cost_brute))
print('Best solution - QAOA        : ' + str(xbest_qaoa) +
      ',  cost = ' + str(-res[best_p].fun))

Best solution - Brute Force : [1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],  cost = 178.96690000000007
Best solution - QAOA        : [0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1],  cost = 111.20050263671858
In [74]:
# Visualising the clusters
x = data_iris_qaoa
y = np.array(xbest_brute)

plt.figure(figsize=(12, 8))
plt.scatter(x[y == 0, 0], x[y == 0, 1], s=100, c='purple', label='Cluster A')
plt.scatter(x[y == 1, 0], x[y == 1, 1], s=100, c='orange', label='Cluster B')
plt.title('Clustering using Brute-Force')
plt.xlabel('sepal length (cm)')
plt.ylabel('sepal width (cm)')
plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))
plt.show()

# Plotting the centroids of the clusters
# plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s=100, c='red', label='Centroids')
# plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))
In [75]:
# Visualising the clusters
x = data_iris_qaoa
y = np.array(xbest_qaoa)

plt.figure(figsize=(12, 8))
plt.scatter(x[y == 0, 0], x[y == 0, 1], s=100, c='purple', label='Cluster A')
plt.scatter(x[y == 1, 0], x[y == 1, 1], s=100, c='orange', label='Cluster B')
plt.title('Clustering using QAOA')
plt.xlabel('sepal length (cm)')
plt.ylabel('sepal width (cm)')
plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))
plt.show()

# Plotting the centroids of the clusters
# plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s=100, c='red', label='Centroids')
# plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))
In [76]:
# Visualising the clusters
x = data_iris_qaoa
y = np.array(data_iris_qaoa_label)

plt.figure(figsize=(12, 8))
plt.scatter(x[y == 0, 0], x[y == 0, 1], s=100,
            c='purple', label='Cluster A(setosa)')
plt.scatter(x[y == 1, 0], x[y == 1, 1], s=100,
            c='orange', label='Cluster B(versicolor)')
plt.scatter(x[y == 2, 0], x[y == 2, 1], s=100,
            c='orange', label='Cluster B(virginica)')
plt.title('Clustering with True labels')
plt.xlabel('sepal length (cm)')
plt.ylabel('sepal width (cm)')
plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))
plt.show()

# Plotting the centroids of the clusters
# plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s=100, c='red', label='Centroids')
# plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))

Comparison with K-means Clustering¶

In [77]:
import os
os.environ["OMP_NUM_THREADS"] = '1'
In [78]:
# Finding the optimum number of clusters for k-means classification
from sklearn.cluster import KMeans
x = data_iris_sample.iloc[:, 0:4]
x
Out[78]:
sepal length (cm) sepal width (cm) petal length (cm) petal width (cm)
8 4.4 2.9 1.4 0.2
14 5.8 4.0 1.2 0.2
15 5.7 4.4 1.5 0.4
27 5.2 3.5 1.5 0.2
33 5.5 4.2 1.4 0.2
35 5.0 3.2 1.2 0.2
114 5.8 2.8 5.1 2.4
117 7.7 3.8 6.7 2.2
125 7.2 3.2 6.0 1.8
126 6.2 2.8 4.8 1.8
140 6.7 3.1 5.6 2.4
141 6.9 3.1 5.1 2.3
In [79]:
# Finding the optimum number of clusters for k-means classification
wcss = []
max_num_cluster = len(data_iris_sample)

for i in range(1, max_num_cluster):
    kmeans = KMeans(n_clusters=i, init='k-means++',
                    max_iter=300, n_init=10, random_state=0)
    kmeans.fit(x)
    wcss.append(kmeans.inertia_)

plt.plot(range(1, max_num_cluster), wcss)
plt.xticks(np.arange(1, max_num_cluster, step=1))  # Set label locations.
plt.title('The elbow method')
plt.xlabel('Number of clusters')
plt.ylabel('Within Cluster Sum of Squares')  # within cluster sum of squares
plt.show()

C:\Users\user1\anaconda3\lib\site-packages\sklearn\cluster\_kmeans.py:1036: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.
  warnings.warn(
In [80]:
num_cluster = 2

kmeans = KMeans(n_clusters=num_cluster, init='k-means++',
                max_iter=300, n_init=10, random_state=0)
y_kmeans = kmeans.fit_predict(x)

x.iloc[0:10, :]

y_kmeans
Out[80]:
array([0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1])
In [81]:
y_kmeans
Out[81]:
array([0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1])
In [82]:
# Visualising the clusters
plt.figure(figsize=(12, 8))
plt.scatter(x.iloc[y_kmeans == 0, 0], x.iloc[y_kmeans ==
            0, 1], s=100, c='purple', label='Cluster A')
plt.scatter(x.iloc[y_kmeans == 1, 0], x.iloc[y_kmeans ==
            1, 1], s=100, c='orange', label='Cluster B')
# plt.scatter(x.iloc[y_kmeans == 2, 0], x.iloc[y_kmeans == 2, 1], s=100, c='green', label='Cluster C')
plt.title('Clustering with K-Means')
plt.xlabel('sepal length (cm)')
plt.ylabel('sepal width (cm)')
plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))


# Plotting the centroids of the clusters
plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[
            :, 1], s=100, marker="v", c='red', label='Centroids')
plt.legend(title="Species",  loc='center left', bbox_to_anchor=(1, 0.5))
plt.show()

Silhoutte Score¶

Code with example¶

In [83]:
from sklearn.cluster import KMeans
import numpy as np
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings('ignore')

np.random.seed(100)
num_data = 50

x11 = np.linspace(0.3, 0.7, 20)
x12 = np.linspace(1.3, 1.8, 15)
x13 = np.linspace(2.4, 3, 15)
x1 = np.concatenate((x11, x12, x13), axis=None)
error = np.random.normal(1, 0.5, num_data)
x2 = 1.5*x1+2+error
In [84]:
fig = plt.figure(figsize=(7, 7))
fig.set_facecolor('white')
plt.scatter(x1, x2, color='k')
plt.xlabel('x1')
plt.ylabel('x2')
plt.show()
In [85]:
X = np.stack([x1, x2], axis=1)
init = np.array([[2., 4.], [1., 5.], [2.5, 6.]])

kmeans = KMeans(n_clusters=3, init=init)
kmeans.fit(X)
labels = kmeans.labels_
In [86]:
def get_silhouette_results(X, labels):
    def get_sum_distance(target_x, target_cluster):
        res = np.sum([np.linalg.norm(target_x-x) for x in target_cluster])
        return res

    '''
    각 데이터 포인트를 돌면서 a(i), b(i)를 계산
    그리고 s(i)를 계산한다.
    
    마지막으로 Silhouette(실루엣) Coefficient를 계산한다.
    '''
    uniq_labels = np.unique(labels)
    silhouette_val_list = []
    for i in range(len(labels)):
        target_data = X[i]

        # calculate a(i)
        target_label = labels[i]
        target_cluster_data_idx = np.where(labels == target_label)[0]
        if len(target_cluster_data_idx) == 1:
            silhouette_val_list.append(0)
            continue
        else:
            target_cluster_data = X[target_cluster_data_idx]
            temp1 = get_sum_distance(target_data, target_cluster_data)
            a_i = temp1/(target_cluster_data.shape[0]-1)

        # calculate b(i)
        b_i_list = []
        label_list = uniq_labels[np.unique(labels) != target_label]
        for ll in label_list:
            other_cluster_data_idx = np.where(labels == ll)[0]
            other_cluster_data = X[other_cluster_data_idx]
            temp2 = get_sum_distance(target_data, other_cluster_data)
            temp_b_i = temp2/other_cluster_data.shape[0]
            b_i_list.append(temp_b_i)

        b_i = min(b_i_list)
        s_i = (b_i-a_i)/max(a_i, b_i)
        silhouette_val_list.append(s_i)

    silhouette_coef_list = []
    for ul in uniq_labels:
        temp3 = np.mean(
            [s for s, l in zip(silhouette_val_list, labels) if l == ul])
        silhouette_coef_list.append(temp3)

    silhouette_coef = max(silhouette_coef_list)
    return (silhouette_coef, np.array(silhouette_val_list))
In [87]:
silhouette_coef, silhouette_val_list = get_silhouette_results(X, labels)
print(silhouette_coef)

0.7434423527756951
In [88]:
import seaborn as sns

# 각 클러스터별로 Silhouette(실루엣) 값을 정렬한다.
uniq_labels = np.unique(labels)
sorted_cluster_svl = []
rearr_labels = []
for ul in uniq_labels:
    labels_idx = np.where(labels == ul)[0]
    target_svl = silhouette_val_list[labels_idx]
    sorted_cluster_svl += sorted(target_svl)
    rearr_labels += [ul]*len(target_svl)

colors = sns.color_palette('hls', len(uniq_labels))
color_labels = [colors[i] for i in rearr_labels]

fig = plt.figure(figsize=(6, 10))
fig.set_facecolor('white')
plt.barh(range(len(sorted_cluster_svl)),
         sorted_cluster_svl, color=color_labels)
plt.ylabel('Data Index')
plt.xlabel('Silhouette Value')
plt.axvline(x=np.mean(sorted_cluster_svl),
            color='black', label='avg. Silhouette score')
plt.text(np.mean(sorted_cluster_svl)+0.02, -1,
         'Avg. \nSilhouette score='+str(round(np.mean(sorted_cluster_svl), 4)))
plt.show()

Brute Force - Silhoutte Score¶

In [89]:
X = data_iris_qaoa
labels = np.array(xbest_brute)
silhouette_coef, silhouette_val_list = get_silhouette_results(X, labels)
print(silhouette_coef)

0.794770113330218
In [90]:
import seaborn as sns

# 각 클러스터별로 Silhouette(실루엣) 값을 정렬한다.
uniq_labels = np.unique(labels)
sorted_cluster_svl = []
rearr_labels = []
for ul in uniq_labels:
    labels_idx = np.where(labels == ul)[0]
    target_svl = silhouette_val_list[labels_idx]
    sorted_cluster_svl += sorted(target_svl)
    rearr_labels += [ul]*len(target_svl)

colors = sns.color_palette('hls', len(uniq_labels))
color_labels = [colors[i] for i in rearr_labels]

fig = plt.figure(figsize=(6, 10))
fig.set_facecolor('white')
plt.barh(range(len(sorted_cluster_svl)),
         sorted_cluster_svl, color=color_labels)
plt.title('Silhoutte Score of Brute Force')
plt.ylabel('Data Index')
plt.xlabel('Silhouette Value')
plt.axvline(x=np.mean(sorted_cluster_svl),
            color='black', label='avg. Silhouette score')
plt.text(np.mean(sorted_cluster_svl)+0.02, -1,
         'Avg. \nSilhouette score='+str(round(np.mean(sorted_cluster_svl), 4)))
plt.show()

QAOA - Silhoutte Score¶

In [91]:
X = data_iris_qaoa
labels = np.array(xbest_qaoa)
silhouette_coef, silhouette_val_list = get_silhouette_results(X, labels)
print(silhouette_coef)

0.2863522180590626
In [92]:
import seaborn as sns

# 각 클러스터별로 Silhouette(실루엣) 값을 정렬한다.
uniq_labels = np.unique(labels)
sorted_cluster_svl = []
rearr_labels = []
for ul in uniq_labels:
    labels_idx = np.where(labels == ul)[0]
    target_svl = silhouette_val_list[labels_idx]
    sorted_cluster_svl += sorted(target_svl)
    rearr_labels += [ul]*len(target_svl)

colors = sns.color_palette('hls', len(uniq_labels))
color_labels = [colors[i] for i in rearr_labels]

fig = plt.figure(figsize=(6, 10))
fig.set_facecolor('white')
plt.barh(range(len(sorted_cluster_svl)),
         sorted_cluster_svl, color=color_labels)
plt.title('Silhoutte Score of QAOA')
plt.ylabel('Data Index')
plt.xlabel('Silhouette Value')
plt.axvline(x=np.mean(sorted_cluster_svl),
            color='black', label='avg. Silhouette score')
plt.text(np.mean(sorted_cluster_svl)+0.02, -1,
         'Avg. \nSilhouette score='+str(round(np.mean(sorted_cluster_svl), 4)))
plt.show()

K-Means - Silhoutte Score¶

In [93]:
X = data_iris_qaoa
labels = y_kmeans
silhouette_coef, silhouette_val_list = get_silhouette_results(X, labels)
print(silhouette_coef)

0.794770113330218
In [94]:
type(xbest_brute)
Out[94]:
list
In [95]:
import seaborn as sns

# 각 클러스터별로 Silhouette(실루엣) 값을 정렬한다.
uniq_labels = np.unique(labels)
sorted_cluster_svl = []
rearr_labels = []
for ul in uniq_labels:
    labels_idx = np.where(labels == ul)[0]
    target_svl = silhouette_val_list[labels_idx]
    sorted_cluster_svl += sorted(target_svl)
    rearr_labels += [ul]*len(target_svl)

colors = sns.color_palette('hls', len(uniq_labels))
color_labels = [colors[i] for i in rearr_labels]

fig = plt.figure(figsize=(6, 10))
fig.set_facecolor('white')
plt.barh(range(len(sorted_cluster_svl)),
         sorted_cluster_svl, color=color_labels)
plt.title('Silhoutte Score of K-Means')
plt.ylabel('Data Index')
plt.xlabel('Silhouette Value')
plt.axvline(x=np.mean(sorted_cluster_svl),
            color='black', label='avg. Silhouette score')
plt.text(np.mean(sorted_cluster_svl)+0.02, -1,
         'Avg. \nSilhouette score='+str(round(np.mean(sorted_cluster_svl), 4)))
plt.show()

True Label- Silhoutte Score¶

In [96]:
data_iris_qaoa_label
data_iris_qaoa_label2 = np.where(
    data_iris_qaoa_label > 1, 1, data_iris_qaoa_label)
data_iris_qaoa_label2
Out[96]:
array([0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1])
In [97]:
X = data_iris_qaoa
labels = data_iris_qaoa_label2
silhouette_coef, silhouette_val_list = get_silhouette_results(X, labels)
print(silhouette_coef)

0.794770113330218
In [98]:
import seaborn as sns

# 각 클러스터별로 Silhouette(실루엣) 값을 정렬한다.
uniq_labels = np.unique(labels)
sorted_cluster_svl = []
rearr_labels = []
for ul in uniq_labels:
    labels_idx = np.where(labels == ul)[0]
    target_svl = silhouette_val_list[labels_idx]
    sorted_cluster_svl += sorted(target_svl)
    rearr_labels += [ul]*len(target_svl)

colors = sns.color_palette('hls', len(uniq_labels))
color_labels = [colors[i] for i in rearr_labels]

fig = plt.figure(figsize=(6, 10))
fig.set_facecolor('white')
plt.barh(range(len(sorted_cluster_svl)),
         sorted_cluster_svl, color=color_labels)
plt.title('Silhoutte Score of True Label')
plt.ylabel('Data Index')
plt.xlabel('Silhouette Value')
plt.axvline(x=np.mean(sorted_cluster_svl),
            color='black', label='avg. Silhouette score')
plt.text(np.mean(sorted_cluster_svl)+0.02, -1,
         'Avg. \nSilhouette score='+str(round(np.mean(sorted_cluster_svl), 4)))
plt.show()
In [ ]:

Dunn Index¶

In [99]:
import numpy as np
import random
import matplotlib.pyplot as plt

from itertools import combinations

Code with example¶

In [100]:
import numpy as np
import random
import matplotlib.pyplot as plt

from itertools import combinations

np.random.seed(100)
num_data = 20

x1 = np.linspace(0.3, 0.7, num_data)
error = np.random.normal(1, 0.5, num_data)
x2 = 1.5*x1+2+error

X = np.stack([x1, x2], axis=1)
X
Out[100]:
array([[0.3       , 2.57511726],
       [0.32105263, 3.65291915],
       [0.34210526, 4.0896758 ],
       [0.36315789, 3.41851882],
       [0.38421053, 4.06697618],
       [0.40526316, 3.86500416],
       [0.42631579, 3.75006352],
       [0.44736842, 3.13603097],
       [0.46842105, 3.60788366],
       [0.48947368, 3.86171125],
       [0.51052632, 3.53677598],
       [0.53157895, 4.01495017],
       [0.55263158, 3.53714984],
       [0.57368421, 4.26894985],
       [0.59473684, 4.22846567],
       [0.61578947, 3.87147864],
       [0.63684211, 3.68962297],
       [0.65789474, 4.50170845],
       [0.67894737, 3.79935324],
       [0.7       , 3.49084088]])
In [101]:
fig = plt.figure(figsize=(7, 7))
fig.set_facecolor('white')
plt.scatter(x1, x2, color='k')
plt.xlabel('x1')
plt.ylabel('x2')
plt.show()
In [ ]:

클러스터 내 거리 측도 Intra-Cluster distance measure¶

  • a. Complete Diameter Distance: This function below calculates the maximum distance between two points within the cluster. (This version was proposed by Dunn).
In [102]:
def complete_diameter_distance(X):
    res = []
    for i, j in combinations(range(X.shape[0]), 2):
        a_i = X[i, :]
        a_j = X[j, :]
        res.append(np.linalg.norm(a_i-a_j))

    return np.max(res)
In [103]:
complete_diameter_distance(X)
Out[103]:
1.9595515390777758
  • b. Average Diamiter Distance: This function calculates the mean distance between all pairs within the same cluster.
In [104]:
def average_diameter_distance(X):
    res = []
    for i, j in combinations(range(X.shape[0]), 2):
        a_i = X[i, :]
        a_j = X[j, :]
        res.append(np.linalg.norm(a_i-a_j))

    return np.mean(res)
In [105]:
average_diameter_distance(X)
Out[105]:
0.5159584769337329
  • c. Average Diamiter Distance: This function calculates distance of all the points from the mean within the cluster.
In [106]:
def centroid_diameter_distance(X):
    center = np.mean(X, axis=0)
    res = 2*np.mean([np.linalg.norm(x-center) for x in X])

    return res
In [107]:
centroid_diameter_distance(X)
Out[107]:
0.6874635793987067

클러스터 간 거리 측도 Inter-Cluster distance measure¶

  • a. Single Linkage Distance: This function below calculates the minimum distance between clusters.
In [108]:
np.random.seed(100)

x11 = np.linspace(0.3, 0.7, 20)
label1 = [0]*len(x11)
x12 = np.linspace(1.3, 1.8, 15)
label2 = [1]*len(x12)
error = np.random.normal(1, 0.5, 35)
x1 = np.concatenate((x11, x12), axis=None)
x2 = 1.5*x1+2+error
labels = label1+label2

X = np.stack((x1, x2), axis=1)

labels = np.array(labels)
X1 = X[np.where(labels == 0)[0], :]
X2 = X[np.where(labels == 1)[0], :]
In [109]:
fig = plt.figure(figsize=(7, 7))
fig.set_facecolor('white')
for i, x in enumerate(X):
    if labels[i] == 0:
        plt.scatter(x[0], x[1], color='blue')
    else:
        plt.scatter(x[0], x[1], color='red')
plt.xlabel('x1')
plt.ylabel('x2')
plt.show()
In [110]:
def single_linkage_distance(X1, X2):
    res = []
    for x1 in X1:
        for x2 in X2:
            res.append(np.linalg.norm(x1-x2))
    return np.min(res)
In [111]:
single_linkage_distance(X1, X2)
Out[111]:
0.7724228550378145
  • b. Complete Linkage Distance: This function below calculates the maximum distance between clusters.
In [112]:
def complete_linkage_distance(X1, X2):
    res = []
    for x1 in X1:
        for x2 in X2:
            res.append(np.linalg.norm(x1-x2))
    return np.max(res)
In [113]:
complete_linkage_distance(X1, X2)
Out[113]:
3.807983171195838
  • c. Average Linkage Distance: This function below calculates the minimum distance between clusters.
In [114]:
def average_linkage_distance(X1, X2):
    res = []
    for x1 in X1:
        for x2 in X2:
            res.append(np.linalg.norm(x1-x2))
    return np.mean(res)
In [115]:
average_linkage_distance(X1, X2)
Out[115]:
2.0502961616379003
  • d. Centroid Linkage Distance: This function below calculates distance between centoids of two clusters.
In [116]:
def centroid_linkage_distance(X1, X2):
    center1 = np.mean(X1, axis=0)
    center2 = np.mean(X2, axis=0)
    return np.linalg.norm(center1-center2)
In [117]:
centroid_linkage_distance(X1, X2)
Out[117]:
2.023846293346597
  • e. Average of Centroids Linkage Distance: This function below calculates average value of the distances between a centroid from one cluster and the data points from other clusters.
In [118]:
def average_of_centroids_linkage_distance(X1, X2):
    center1 = np.mean(X1, axis=0)
    center2 = np.mean(X2, axis=0)
    res = []
    for x1 in X1:
        res.append(np.linalg.norm(x1-center2))
    for x2 in X2:
        res.append(np.linalg.norm(x2-center1))

    return np.mean(res)
In [119]:
average_of_centroids_linkage_distance(X1, X2)
Out[119]:
2.035733790732974

Dunn Index 파이썬 구현¶

In [120]:
np.random.seed(100)
num_data = 50

x11 = np.linspace(0.3, 0.7, 20)
label1 = [0]*len(x11)
x12 = np.linspace(1.3, 1.8, 15)
label2 = [1]*len(x12)
x13 = np.linspace(2.4, 3, 15)
label3 = [2]*len(x13)
x1 = np.concatenate((x11, x12, x13), axis=None)
error = np.random.normal(1, 0.5, num_data)
x2 = 1.5*x1+2+error

X = np.stack((x1, x2), axis=1)
labels = np.array(label1+label2+label3)
In [121]:
fig = plt.figure(figsize=(7, 7))
fig.set_facecolor('white')
for i, x in enumerate(X):
    if labels[i] == 0:
        plt.scatter(x[0], x[1], color='blue')
    elif labels[i] == 1:
        plt.scatter(x[0], x[1], color='red')
    else:
        plt.scatter(x[0], x[1], color='green')
plt.xlabel('x1')
plt.ylabel('x2')
plt.show()
In [122]:
def Dunn_index(X, labels, intra_cluster_distance_type, inter_cluster_distance_type):
    intra_cdt_dict = {
        'cmpl_dd': complete_diameter_distance,
        'avdd': average_diameter_distance,
        'cent_dd': centroid_diameter_distance
    }
    inter_cdt_dict = {
        'sld': single_linkage_distance,
        'cmpl_ld': complete_linkage_distance,
        'avld': average_linkage_distance,
        'cent_ld': centroid_linkage_distance,
        'av_cent_ld': average_of_centroids_linkage_distance
    }
    # intra cluster distance
    intra_cluster_distance = intra_cdt_dict[intra_cluster_distance_type]

    # inter cluster distance
    inter_cluster_distance = inter_cdt_dict[inter_cluster_distance_type]

    # get minimum value of inter_cluster_distance
    res1 = []
    for i, j in combinations(np.unique(labels), 2):
        X1 = X[np.where(labels == i)[0], :]
        X2 = X[np.where(labels == j)[0], :]
        res1.append(inter_cluster_distance(X1, X2))
    min_inter_cd = np.min(res1)

    # get maximum value of intra_cluser_distance

    res2 = []
    for label in np.unique(labels):
        X_target = X[np.where(labels == label)[0], :]
        if X_target.shape[0] >= 2:
            res2.append(intra_cluster_distance(X_target))
        else:
            res2.append(0)
    max_intra_cd = np.max(res2)

    Dunn_idx = min_inter_cd/max_intra_cd
    return Dunn_idx
In [123]:
intra_cluster_distance_type = ['cmpl_dd', 'avdd', 'cent_dd']
inter_cluster_distance_type = [
    'sld', 'cmpl_ld', 'avld', 'cent_ld', 'av_cent_ld']

for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        print("Dunn Index:", "Intra Cluster Dist.:", '%-10s' % intra_cluster_distance_type[i],
              "Inter Cluster Dist.:", '%-12s' % inter_cluster_distance_type[j],
              "Dunn Index Valule:", Dunn_index(X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j]))

Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 0.2780279425885912
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 1.5816104606529293
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 0.7627361333011984
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 0.7374610426286897
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 0.7486880384584048
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: sld          Dunn Index Valule: 0.8233205335652861
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 4.683602504961463
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: avld         Dunn Index Valule: 2.2586806002025015
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cent_ld      Dunn Index Valule: 2.1838338026300956
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 2.2170801594919096
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 0.6140262424157213
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 3.492995412900513
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 1.6845069510824404
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 1.6286867741323774
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 1.6534816562537682
In [124]:
import random
import pandas as pd

# 빈 DataFrame 생성하기
Dunn_Index_result = pd.DataFrame(
    columns=['intra cluster', 'inter cluster', 'Dunn index'])
Dunn_Index_result
Out[124]:
intra cluster inter cluster Dunn index
In [125]:
len(inter_cluster_distance_type)
Out[125]:
5
In [126]:
for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        Dunn_Index_result.loc[len(inter_cluster_distance_type)
                              * i+j, 'intra cluster'] = intra_cluster_distance_type[i]
        Dunn_Index_result.loc[len(inter_cluster_distance_type)
                              * i+j, 'inter cluster'] = inter_cluster_distance_type[j],
        Dunn_Index_result.loc[len(inter_cluster_distance_type)*i+j, 'Dunn index'] = Dunn_index(
            X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j])

Dunn_Index_result
Out[126]:
intra cluster inter cluster Dunn index
0 cmpl_dd (sld,) 0.278028
1 cmpl_dd (cmpl_ld,) 1.58161
2 cmpl_dd (avld,) 0.762736
3 cmpl_dd (cent_ld,) 0.737461
4 cmpl_dd (av_cent_ld,) 0.748688
5 avdd (sld,) 0.823321
6 avdd (cmpl_ld,) 4.683603
7 avdd (avld,) 2.258681
8 avdd (cent_ld,) 2.183834
9 avdd (av_cent_ld,) 2.21708
10 cent_dd (sld,) 0.614026
11 cent_dd (cmpl_ld,) 3.492995
12 cent_dd (avld,) 1.684507
13 cent_dd (cent_ld,) 1.628687
14 cent_dd (av_cent_ld,) 1.653482
In [127]:
Dunn_Index_result[Dunn_Index_result['Dunn index']
                  == Dunn_Index_result['Dunn index'].max()]
Out[127]:
intra cluster inter cluster Dunn index
6 avdd (cmpl_ld,) 4.683603
In [ ]:

Brute Force - Dunn Index¶

In [128]:
X = data_iris_qaoa
labels = np.array(xbest_brute)

for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        print("Dunn Index:", "Intra Cluster Dist.:", '%-10s' % intra_cluster_distance_type[i],
              "Inter Cluster Dist.:", '%-12s' % inter_cluster_distance_type[j],
              "Dunn Index Valule:", Dunn_index(X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j]))

Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 1.4394867323822669
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 2.464449028739809
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 1.8514118502628683
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 1.8128558392017404
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 1.8320706056393765
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: sld          Dunn Index Valule: 2.7497575705234842
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 4.707676160885204
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: avld         Dunn Index Valule: 3.5366312428541895
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cent_ld      Dunn Index Valule: 3.4629802109137517
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 3.4996849253714455
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 2.1864618020548283
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 3.743295122653327
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 2.812142133308962
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 2.7535787276669765
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 2.7827643755136697
In [129]:
# 빈 DataFrame 생성하기
Dunn_Index_result_brute = pd.DataFrame(columns=['intra cluster', 'inter cluster', 'Dunn index'])
Dunn_Index_result_brute
Out[129]:
intra cluster inter cluster Dunn index
In [130]:
for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        Dunn_Index_result_brute.loc[len(inter_cluster_distance_type)
                              * i+j, 'intra cluster'] = intra_cluster_distance_type[i]
        Dunn_Index_result_brute.loc[len(inter_cluster_distance_type)
                              * i+j, 'inter cluster'] = inter_cluster_distance_type[j]
        Dunn_Index_result_brute.loc[len(inter_cluster_distance_type)*i+j, 'Dunn index'] = Dunn_index(
            X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j])

Dunn_Index_result_brute
Out[130]:
intra cluster inter cluster Dunn index
0 cmpl_dd sld 1.439487
1 cmpl_dd cmpl_ld 2.464449
2 cmpl_dd avld 1.851412
3 cmpl_dd cent_ld 1.812856
4 cmpl_dd av_cent_ld 1.832071
5 avdd sld 2.749758
6 avdd cmpl_ld 4.707676
7 avdd avld 3.536631
8 avdd cent_ld 3.46298
9 avdd av_cent_ld 3.499685
10 cent_dd sld 2.186462
11 cent_dd cmpl_ld 3.743295
12 cent_dd avld 2.812142
13 cent_dd cent_ld 2.753579
14 cent_dd av_cent_ld 2.782764
In [131]:
Dunn_Index_result_brute[Dunn_Index_result_brute['Dunn index']== Dunn_Index_result_brute['Dunn index'].max()]
Out[131]:
intra cluster inter cluster Dunn index
6 avdd cmpl_ld 4.707676

QAOA - Dunn Index¶

In [132]:
X = data_iris_qaoa
labels = np.array(xbest_qaoa)

for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        print("Dunn Index:", "Intra Cluster Dist.:", '%-10s' % intra_cluster_distance_type[i],
              "Inter Cluster Dist.:", '%-12s' % inter_cluster_distance_type[j],
              "Dunn Index Valule:", Dunn_index(X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j]))

Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 0.05570121451395257
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 1.0223049440201388
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 0.5488613350100602
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 0.4107329707129978
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 0.49808485775425215
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: sld          Dunn Index Valule: 0.11486400418326687
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 2.1081414542063466
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: avld         Dunn Index Valule: 1.13183188608638
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cent_ld      Dunn Index Valule: 0.8469911128125529
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 1.0271234062656802
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 0.0828607015393091
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 1.5207730313922356
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 0.8164819324602577
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 0.6110032320763569
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 0.7409472324752668
In [133]:
# 빈 DataFrame 생성하기
Dunn_Index_result_qaoa = pd.DataFrame(columns=['intra cluster', 'inter cluster', 'Dunn index'])
Dunn_Index_result_qaoa
Out[133]:
intra cluster inter cluster Dunn index
In [134]:
for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        Dunn_Index_result_qaoa.loc[len(inter_cluster_distance_type)
                              * i+j, 'intra cluster'] = intra_cluster_distance_type[i]
        Dunn_Index_result_qaoa.loc[len(inter_cluster_distance_type)
                              * i+j, 'inter cluster'] = inter_cluster_distance_type[j]
        Dunn_Index_result_qaoa.loc[len(inter_cluster_distance_type)*i+j, 'Dunn index'] = Dunn_index(
            X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j])

Dunn_Index_result_qaoa
Out[134]:
intra cluster inter cluster Dunn index
0 cmpl_dd sld 0.055701
1 cmpl_dd cmpl_ld 1.022305
2 cmpl_dd avld 0.548861
3 cmpl_dd cent_ld 0.410733
4 cmpl_dd av_cent_ld 0.498085
5 avdd sld 0.114864
6 avdd cmpl_ld 2.108141
7 avdd avld 1.131832
8 avdd cent_ld 0.846991
9 avdd av_cent_ld 1.027123
10 cent_dd sld 0.082861
11 cent_dd cmpl_ld 1.520773
12 cent_dd avld 0.816482
13 cent_dd cent_ld 0.611003
14 cent_dd av_cent_ld 0.740947
In [135]:
Dunn_Index_result_qaoa[Dunn_Index_result_qaoa['Dunn index']== Dunn_Index_result_qaoa['Dunn index'].max()]
Out[135]:
intra cluster inter cluster Dunn index
6 avdd cmpl_ld 2.108141

K-Means - Dunn Index¶

In [136]:
X = data_iris_qaoa
labels = y_kmeans

for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        print("Dunn Index:", "Intra Cluster Dist.:", '%-10s' % intra_cluster_distance_type[i],
              "Inter Cluster Dist.:", '%-12s' % inter_cluster_distance_type[j],
              "Dunn Index Valule:", Dunn_index(X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j]))

Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 1.4394867323822669
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 2.464449028739809
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 1.8514118502628678
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 1.8128558392017404
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 1.8320706056393767
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: sld          Dunn Index Valule: 2.7497575705234842
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 4.707676160885204
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: avld         Dunn Index Valule: 3.536631242854189
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cent_ld      Dunn Index Valule: 3.4629802109137517
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 3.4996849253714464
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 2.1864618020548283
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 3.743295122653327
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 2.8121421333089613
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 2.7535787276669765
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 2.78276437551367
In [137]:
# 빈 DataFrame 생성하기
Dunn_Index_result_kmeans = pd.DataFrame(columns=['intra cluster', 'inter cluster', 'Dunn index'])
Dunn_Index_result_kmeans
Out[137]:
intra cluster inter cluster Dunn index
In [138]:
for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        Dunn_Index_result_kmeans.loc[len(inter_cluster_distance_type)
                              * i+j, 'intra cluster'] = intra_cluster_distance_type[i]
        Dunn_Index_result_kmeans.loc[len(inter_cluster_distance_type)
                              * i+j, 'inter cluster'] = inter_cluster_distance_type[j]
        Dunn_Index_result_kmeans.loc[len(inter_cluster_distance_type)*i+j, 'Dunn index'] = Dunn_index(
            X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j])

Dunn_Index_result_kmeans
Out[138]:
intra cluster inter cluster Dunn index
0 cmpl_dd sld 1.439487
1 cmpl_dd cmpl_ld 2.464449
2 cmpl_dd avld 1.851412
3 cmpl_dd cent_ld 1.812856
4 cmpl_dd av_cent_ld 1.832071
5 avdd sld 2.749758
6 avdd cmpl_ld 4.707676
7 avdd avld 3.536631
8 avdd cent_ld 3.46298
9 avdd av_cent_ld 3.499685
10 cent_dd sld 2.186462
11 cent_dd cmpl_ld 3.743295
12 cent_dd avld 2.812142
13 cent_dd cent_ld 2.753579
14 cent_dd av_cent_ld 2.782764
In [139]:
Dunn_Index_result_kmeans[Dunn_Index_result_kmeans['Dunn index']== Dunn_Index_result_kmeans['Dunn index'].max()]
Out[139]:
intra cluster inter cluster Dunn index
6 avdd cmpl_ld 4.707676

True Label - Dunn Index¶

In [140]:
X = data_iris_qaoa
labels = data_iris_qaoa_label2

for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        print("Dunn Index:", "Intra Cluster Dist.:", '%-10s' % intra_cluster_distance_type[i],
              "Inter Cluster Dist.:", '%-12s' % inter_cluster_distance_type[j],
              "Dunn Index Valule:", Dunn_index(X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j]))

Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 1.4394867323822669
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 2.464449028739809
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 1.8514118502628678
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 1.8128558392017404
Dunn Index: Intra Cluster Dist.: cmpl_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 1.8320706056393767
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: sld          Dunn Index Valule: 2.7497575705234842
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 4.707676160885204
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: avld         Dunn Index Valule: 3.536631242854189
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: cent_ld      Dunn Index Valule: 3.4629802109137517
Dunn Index: Intra Cluster Dist.: avdd       Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 3.4996849253714464
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: sld          Dunn Index Valule: 2.1864618020548283
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cmpl_ld      Dunn Index Valule: 3.743295122653327
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: avld         Dunn Index Valule: 2.8121421333089613
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: cent_ld      Dunn Index Valule: 2.7535787276669765
Dunn Index: Intra Cluster Dist.: cent_dd    Inter Cluster Dist.: av_cent_ld   Dunn Index Valule: 2.78276437551367
In [141]:
# 빈 DataFrame 생성하기
Dunn_Index_result_truelabel = pd.DataFrame(columns=['intra cluster', 'inter cluster', 'Dunn index'])
Dunn_Index_result_truelabel
Out[141]:
intra cluster inter cluster Dunn index
In [142]:
for i in range(len(intra_cluster_distance_type)):
    for j in range(len(inter_cluster_distance_type)):
        Dunn_Index_result_truelabel.loc[len(inter_cluster_distance_type)
                              * i+j, 'intra cluster'] = intra_cluster_distance_type[i]
        Dunn_Index_result_truelabel.loc[len(inter_cluster_distance_type)
                              * i+j, 'inter cluster'] = inter_cluster_distance_type[j]
        Dunn_Index_result_truelabel.loc[len(inter_cluster_distance_type)*i+j, 'Dunn index'] = Dunn_index(
            X, labels, intra_cluster_distance_type[i], inter_cluster_distance_type[j])

Dunn_Index_result_truelabel
Out[142]:
intra cluster inter cluster Dunn index
0 cmpl_dd sld 1.439487
1 cmpl_dd cmpl_ld 2.464449
2 cmpl_dd avld 1.851412
3 cmpl_dd cent_ld 1.812856
4 cmpl_dd av_cent_ld 1.832071
5 avdd sld 2.749758
6 avdd cmpl_ld 4.707676
7 avdd avld 3.536631
8 avdd cent_ld 3.46298
9 avdd av_cent_ld 3.499685
10 cent_dd sld 2.186462
11 cent_dd cmpl_ld 3.743295
12 cent_dd avld 2.812142
13 cent_dd cent_ld 2.753579
14 cent_dd av_cent_ld 2.782764
In [143]:
Dunn_Index_result_truelabel[Dunn_Index_result_truelabel['Dunn index']== Dunn_Index_result_truelabel['Dunn index'].max()]
Out[143]:
intra cluster inter cluster Dunn index
6 avdd cmpl_ld 4.707676
In [144]:
Dunn_Index_results_combined = Dunn_Index_result_brute[['intra cluster', 'inter cluster']]
Dunn_Index_results_combined['Dunn index - Brute'] = Dunn_Index_result_brute['Dunn index']
Dunn_Index_results_combined['Dunn index - QAOA'] = Dunn_Index_result_qaoa['Dunn index']
Dunn_Index_results_combined['Dunn index - K-Means'] = Dunn_Index_result_kmeans['Dunn index']
Dunn_Index_results_combined['Dunn index - True label'] = Dunn_Index_result_truelabel['Dunn index']

Dunn_Index_results_combined
Out[144]:
intra cluster inter cluster Dunn index - Brute Dunn index - QAOA Dunn index - K-Means Dunn index - True label
0 cmpl_dd sld 1.439487 0.055701 1.439487 1.439487
1 cmpl_dd cmpl_ld 2.464449 1.022305 2.464449 2.464449
2 cmpl_dd avld 1.851412 0.548861 1.851412 1.851412
3 cmpl_dd cent_ld 1.812856 0.410733 1.812856 1.812856
4 cmpl_dd av_cent_ld 1.832071 0.498085 1.832071 1.832071
5 avdd sld 2.749758 0.114864 2.749758 2.749758
6 avdd cmpl_ld 4.707676 2.108141 4.707676 4.707676
7 avdd avld 3.536631 1.131832 3.536631 3.536631
8 avdd cent_ld 3.46298 0.846991 3.46298 3.46298
9 avdd av_cent_ld 3.499685 1.027123 3.499685 3.499685
10 cent_dd sld 2.186462 0.082861 2.186462 2.186462
11 cent_dd cmpl_ld 3.743295 1.520773 3.743295 3.743295
12 cent_dd avld 2.812142 0.816482 2.812142 2.812142
13 cent_dd cent_ld 2.753579 0.611003 2.753579 2.753579
14 cent_dd av_cent_ld 2.782764 0.740947 2.782764 2.782764
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